diff --git a/abelianity_special_kahler_v2.txt b/abelianity_special_kahler_v2.txt
index c512577..1109a26 100644
--- a/abelianity_special_kahler_v2.txt
+++ b/abelianity_special_kahler_v2.txt
@@ -2,8 +2,8 @@
 
 Exercise: The main theorem. What does the abelianity conjecture say, and is it proven here?
 Campana's abelianity conjecture predicts that the fundamental group of any special compact Kähler manifold has an abelian subgroup of finite index. The paper proves it in full: for every connected smooth compact Kähler manifold X, if X is special, then π₁(X) is virtually abelian. Equivalently, there is a connected finite unramified cover X' → X with π₁(X') abelian. No projectivity, no linearity, no residual finiteness, no prescribed Kodaira dimension is assumed; the finite index and the cover are allowed to depend on X; torsion in π₁(X) is allowed.
-Claudon-Höring 2013, Compact Kähler manifolds with compactifiable universal cover: https://doi.org/10.24033/bsmf.2651
-Campana 2004, Orbifolds, special varieties and classification theory: https://arxiv.org/abs/math/0110051
+Claudon-Höring 2013, Compact Kähler manifolds with compactifiable universal cover: ./pdf/claudon-horing-2013-compact-kahler-manifolds-with-compactifiable-universal-cover.pdf
+Campana 2004, Orbifolds, special varieties and classification theory: ./pdf/campana-2004-math0110051-orbifolds-special-varieties-and-classification-theory.pdf
 
 Exercise: Kähler manifold. What is a compact Kähler manifold, and what are the basic examples?
 A complex manifold is a topological space locally modelled on ℂⁿ with holomorphic transition maps. It has real dimension 2n. A Kähler structure is a Riemannian metric whose associated 2-form is closed, which forces compatibility between metric and complex structure. Compactness means every open cover has a finite subcover (in ℝⁿ, by Heine-Borel, this is equivalent to closed and bounded). Examples: complex projective space Pⁿ, complex tori ℂⁿ/Λ, smooth hypersurfaces in projective space, all compact Riemann surfaces. The Kähler condition buys strong global Hodge theory, which is used in the deep input theorems.
@@ -28,11 +28,11 @@ For our purposes, a sheaf on X assigns to each open set U a vector space (or abe
 Exercise: Bogomolov sheaf. What is a Bogomolov sheaf?
 A Bogomolov sheaf on a compact Kähler X is a nonzero sheaf morphism L → Ω^p_X from a line bundle L to the sheaf of holomorphic p-forms, with κ(X, L) = p for some 1 ≤ p ≤ dim X. Bogomolov's theorem gives κ(X, L) ≤ p always; equality means "the p-form image has an Iitaka dimension as large as possible", which is a strong positivity property. Such a sheaf exhibits X as having a positive-dimensional "general type base" hidden inside the p-form data. Specialness is exactly the absence of Bogomolov sheaves.
 Bogomolov 1979, Holomorphic tensors and vector bundles on projective varieties: https://www.mathnet.ru/eng/im1965
-Campana 2004, Orbifolds, special varieties and classification theory: https://arxiv.org/abs/math/0110051
+Campana 2004, Orbifolds, special varieties and classification theory: ./pdf/campana-2004-math0110051-orbifolds-special-varieties-and-classification-theory.pdf
 
 Exercise: Special. What is a special compact Kähler manifold?
 Let X be compact Kähler of complex dimension n. X is special if for every 1 ≤ p ≤ n and every nonzero sheaf morphism L → Ω^p_X from a line bundle L, one has κ(X, L) ≤ p − 1 (i.e., strictly less than p). Equivalently, X is special iff there is no Bogomolov sheaf on X. A point is special. Pⁿ is special. Every Calabi-Yau and irreducible symplectic manifold is special. Conversely, all smooth compact Kähler manifolds of general type (κ = n) and all fibrations onto a general type base contain a Bogomolov sheaf, so they are not special.
-Campana 2004, Orbifolds, special varieties and classification theory: https://arxiv.org/abs/math/0110051
+Campana 2004, Orbifolds, special varieties and classification theory: ./pdf/campana-2004-math0110051-orbifolds-special-varieties-and-classification-theory.pdf
 
 Exercise: Why "special". What is the intuition behind the name?
 Campana's classification program partitions every compact Kähler manifold into a base of general type plus "special" fibres, in analogy with the classification of curves (base = curve of Riemann surface, fibres = genus 0 or 1) and surfaces. On a manifold of general type, holomorphic tensors with κ = p detect the "base" completely, so the fundamental group sees a piece of it. The conjecture says special manifolds should have "hidden rigidity" in the opposite direction: their π₁ has no interesting non-abelian behaviour after finite covers. The paper makes this precise.
@@ -45,16 +45,16 @@ Ueno 1975, Classification Theory of Algebraic Varieties and Compact Complex Spac
 
 Exercise: Albanese surjectivity. Why is the Albanese map of a special X surjective with connected fibres?
 Campana's 2004 paper proved this, but there was an error in the treatment of multiple fibres; the 2023 correction restores surjectivity and connectedness for Kähler special manifolds. The nonprojective Albanese torus requires careful meridian bookkeeping, which the paper does not avoid—it uses actual meridian orders throughout Section descent.tex. The corrected result is all the paper needs from that direction.
-Campana 2004, Orbifolds, special varieties and classification theory: https://arxiv.org/abs/math/0110051
-Campana 2023, Albanese map of special manifolds: a correction: https://www.numdam.org/item/10.5802/aif.3563
+Campana 2004, Orbifolds, special varieties and classification theory: ./pdf/campana-2004-math0110051-orbifolds-special-varieties-and-classification-theory.pdf
+Campana 2023, Albanese map of special manifolds: a correction: ./pdf/campana-2023-albanese-map-of-special-manifolds-a-correction.pdf
 
 Exercise: Maximal b₁. Why can one choose a finite cover with maximal first Betti number, and what does it give?
 Specialness is preserved by finite étale covers (Campana 2004) and finite étale covers of compact Kähler manifolds are compact Kähler. Every special X has surjective Albanese, so b_1(X) ≤ 2 dim X. Choose a finite étale cover X' → X with b_1(X') maximal. Pullback along a finite unramified cover is injective on H¹(−, ℚ) by transfer, and if X'' → X' were a cover with larger b_1, then X'' → X is a cover of X with larger b_1, contradicting maximality. So all further covers have b_1 = b_1(X'). One may work on X' with this convenient property.
-Campana 2004, Orbifolds, special varieties and classification theory: https://arxiv.org/abs/math/0110051
+Campana 2004, Orbifolds, special varieties and classification theory: ./pdf/campana-2004-math0110051-orbifolds-special-varieties-and-classification-theory.pdf
 
 Exercise: Albanese exactness. State the exact sequence and sketch its proof.
 Let α: X → A = Alb(X), G = π₁(X), S = a smooth general Albanese fibre, N = im(π₁(S) → G). Then 1 → N → G → π₁(A) → 1 is exact (Lemma: Albanese Exactness). Proof: over the smooth Albanese fibration locus, the homotopy exact sequence of a smooth proper family gives exactness after passing to the open space. The monodromy homomorphism ψ: π₁(A°) → R = G/N has finite-order image at every meridian, since a loop around the discriminant lifts to a loop in X whose image is killed by N. Filling in the discriminant gives a well-defined map π₁(A) → R; the natural map G → R = G/N factors through π₁(A), and the two factorizations are inverse, so R ≅ π₁(A). The case A = {pt} reduces to N = G.
-Juanyong Wang 2021, On the Iitaka conjecture C_{n,m} for Kähler fibre spaces: https://www.numdam.org/item/AFST_2021_6_30_4_813_0
+Juanyong Wang 2021, On the Iitaka conjecture C_{n,m} for Kähler fibre spaces: ./pdf/juanyong-wang-2021-on-the-iitaka-conjecture-c-n-m.pdf
 
 Exercise: N normal. Why is N normal in G, and finitely generated?
 Over a smooth Albanese fibration locus, the homotopy exact sequence makes N = ker(π₁(X) → π₁(A)) normal in G. The group N is finitely generated because the general Albanese fibre S is a compact complex manifold, and the fundamental group of any compact manifold is finitely presented. Base-point transport in the smooth proper family changes N up to conjugation, which does not affect normalcy.
@@ -65,7 +65,7 @@ A group N is FAb if every finite-index subgroup of N has finite abelianization (
 
 Exercise: N is FAb. Sketch the proof, with the role of Botong Wang's theorem.
 Proposition (Fiber FAb): N is FAb. Pass to a finite-index cover X', let N' = N ∩ π₁(X'), Λ = π₁(A), V = Hom(N', ℂ) (a finite-dim. complex vector space, since N' is finitely generated). Λ acts on V by conjugation; write T_λ for the operator on V. For a finite-order character β: Λ → ℂ*, the Koszul resolution of Λ with coefficients in ℂ_β is contractible, so H^q(Λ, ℂ_β) = 0 for all q > 0. Inflation-restriction therefore identifies H¹(G', ℂ_β) ≅ (V ⊗ ℂ_β)^Λ. Now suppose V ≠ 0: the commuting T_λ have a common eigenvector v with nonzero eigenvalue, defining a character χ. If χ ≠ 1 then H¹(G', ℂ_β) ≠ 0 for β = χ^{−1}, and Botong Wang's torsion-translate theorem says this support point is a torsion character of Λ. Kill χ by an isogeny A_0 → A and pull back to a cover X_0; the argument descends, keeping V ≠ 0. Now V^Λ ≠ 0. Untwisted inflation-restriction gives an exact sequence 0 → H¹(Λ, ℂ) → H¹(G', ℂ) → V^Λ → H²(Λ, ℂ) → H²(G', ℂ), and the pullback map H²(A') → H²(X') is injective (Kähler fibre integration plus Poincaré duality), which forces V^Λ = 0. Combined with V = 0, this proves Hom(N', ℂ) = 0 for every finite-index N'. Since N' is finitely generated, its abelianization is finite; N is FAb.
-Botong Wang 2016, Torsion points on the cohomology jump loci of compact Kähler manifolds: https://arxiv.org/abs/1312.6619
+Botong Wang 2016, Torsion points on the cohomology jump loci of compact Kähler manifolds: ./pdf/botong-wang-2016-1312.6619-torsion-points-on-the-cohomology-jump-loci.pdf
 
 Exercise: Finite-by-abelian. State the finite-by-abelian lemma.
 If 1 → F → E → ℤ^r → 1 is exact and F is finite, then E is virtually abelian and residually finite. In particular E has a finite-index subgroup disjoint from F. Proof (Lemma: Finite-by-Abelian): the centralizer E_0 of F has finite index; its commutator is central in F, so powers of generators of E_0 commute. Pass to the abelian subgroup generated by large powers and to its core in E; intersect sufficiently many conjugates to separate F.
@@ -78,62 +78,62 @@ Suppose the Albanese exact sequence 1 → N → G → ℤ^r → 1 has finite N.
 
 Exercise: Γ-reduction. What is Campana's Γ-reduction?
 Given a homomorphism ρ: π₁(M) → P from a smooth compact Kähler manifold, there is a fibration γ_ρ: M ⇢ B_ρ with connected general fibre, Kähler base model B_ρ, such that a smooth general fibre has finite ρ-image, and γ_ρ contracts every compact irreducible subvariety through a very general point whose π₁ has finite ρ-image. dim B_ρ is the Γ-dimension γd(M, ρ). ρ is generically large if γd(M, ρ) = dim M. The theorem is due to Campana; the arbitrary-quotient form is used in the paper.
-Campana 1994, Remarques sur le revêtement universel des variétés kählériennes compactes: https://www.numdam.org/item/10.24033/bsmf.2232
-CCE 2015, Linear representations of Kähler groups: https://arxiv.org/abs/1302.5016
+Campana 1994, Remarques sur le revêtement universel des variétés kählériennes compactes: ./pdf/campana-1994-remarques-sur-le-revetement-universel-des-varietes.pdf
+CCE 2015, Linear representations of Kähler groups: ./pdf/cce-2015-1302.5016-linear-representations-of-kahler-groups.pdf
 
 Exercise: Minimal ℓ. What is minimized, and how does a Barlet-type space give the factorized map?
 Assume N is infinite. Consider all finite étale covers X' → X and all fibrations S ⇢ T of a very general good Albanese fibre S, where C = im(π₁(T) → N) and N/C is infinite. Minimize ℓ = dim T over all such data. The identity fibration S ⇢ {pt} is admissible (N infinite), so ℓ ≥ 1. Compactified family language (Barlet space of compact analytic cycles, Campana's meromorphic Γ-reduction) globalizes the minimizer to a factorization X ⇢ Z →^g A with connected general fibres and dim Z − dim A = ℓ (Proposition: Minimal Base).
 Barlet 1975, Espace analytique réduit des cycles analytiques complexes compacts: https://doi.org/10.1007/BFb0080243
-Campana 1994, Remarques sur le revêtement universel des variétés kählériennes compactes: https://www.numdam.org/item/10.24033/bsmf.2232
+Campana 1994, Remarques sur le revêtement universel des variétés kählériennes compactes: ./pdf/campana-1994-remarques-sur-le-revetement-universel-des-varietes.pdf
 
 Exercise: Inertial boundary. What is Δ_Z on a prepared model of Z?
 Fix R = G/B_0 where B_0 is the actual group image of the general Z-fibre group. On a prepared smooth model Z (smooth compact Kähler, resolved source, SNC deleted divisor, maps holomorphically to A), for a prime divisor D ⊂ Z let m_D be the order in R of a meridian around a general point of D under the compatible monodromy ψ: π₁(Z°) → R. The inertial boundary is Δ_Z = ∑_D (1 − 1/m_D) D. It is a ℚ-Cartier divisor with SNC support and coefficients in [0,1); the pair (Z, Δ_Z) is klt. On a very general good Albanese fibre Y ⊂ Z, the restriction Δ_Y = Δ_Z|_Y has the same integer meridians, and the same order.
-Juanyong Wang 2021, On the Iitaka conjecture C_{n,m} for Kähler fibre spaces: https://www.numdam.org/item/AFST_2021_6_30_4_813_0
+Juanyong Wang 2021, On the Iitaka conjecture C_{n,m} for Kähler fibre spaces: ./pdf/juanyong-wang-2021-on-the-iitaka-conjecture-c-n-m.pdf
 
 Exercise: Two cases. What is the case distinction after minimality?
 The quotient Q = N/B_0 is an infinite FAb subgroup of R. Either every finite-dimensional complex linear image of Q is finite ("Case A"), or Q has an infinite complex linear image ("Case B"). In Case A, L² spectral analysis plus Hilbert tensor positivity produces a big cotangent line on Y, hence K_Y + Δ_Y big. In Case B, FAb rules out virtually solvable images, Selberg's lemma produces a torsion-free image in a simple semisimple group, and CCE linear general-type gives K_Y big. Both cases then contradict torus descent.
 
 Exercise: Spectral theorem. What does "zero in the Dolbeault spectrum" mean?
 Theorem (Zero in the Dolbeault Spectrum): if M is a connected compact Kähler orbifold and U → M a connected normal orbifold cover with infinite deck group P, then in some (p, 0) degree zero belongs to the L² spectrum of the Dolbeault Laplacian Δ'' on scalar (p, 0)-forms. Equivalently, there are L² (p, 0)-forms on U with Δ''-eigenvalues → 0 (equivalently, the infimum of the spectrum is zero). The proof places the diagonal {(u, u)} into the compact quotient D = (U × U)/P; a positive lower bound on the spectral gap would let weighted smoothing shrink the pairing of its class with the diagonal test form to zero while preserving the class—impossible. Weighted Monge–Ampère potentials with cellwise exponential integrability are used. This is the building block for constructing holomorphic tensors with Hilbert coefficients.
-Atiyah 1976, Elliptic operators, discrete groups and von Neumann algebras: https://www.numdam.org/item/AST_1976__32-33__43_0.pdf
+Atiyah 1976, Elliptic operators, discrete groups and von Neumann algebras: ./pdf/iyah-1976-elliptic-operators-discrete-groups-and-von-neumann.pdf
 Dodziuk 1977, De Rham–Hodge theory for L²-cohomology of infinite coverings: https://doi.org/10.1016/0040-9383(77)90013-1
 
 Exercise: Spectral → Hilbert tensors. How does the spectral theorem produce nonzero holomorphic Hilbert-valued tensors?
 Fold low-spectrum (p, 0)-forms on a normal orbifold cover U → Y down to the compact base, using the regular representation λ_Q of Q on ℓ²(Q). The result is a holomorphic section of Ω^p_Y ⊗ λ_Q in the ultrapower as the spectral parameter → 0. Taking an exterior power / rank-minimalization gives a line tensor. For the amenable case, Shalom's reduced-cohomology theorem produces the analogous Hilbert coefficient. Combine to get Proposition (Hilbert Coefficients): a separable unitary representation ρ: Q → U(H) with no nonzero finite-dim. invariant subspace and a nonzero holomorphic section of Ω^p_Y ⊗ H_ρ over the orbifold.
-Shalom 2006, The algebraization of Kazhdan's property (T): https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2006.2/ICM2006.2.ocr.pdf
-Atiyah 1976, Elliptic operators, discrete groups and von Neumann algebras: https://www.numdam.org/item/AST_1976__32-33__43_0.pdf
+Shalom 2006, The algebraization of Kazhdan's property (T): ./pdf/shalom-2006-the-algebraization-of-kazhdan-s-property-t.pdf
+Atiyah 1976, Elliptic operators, discrete groups and von Neumann algebras: ./pdf/iyah-1976-elliptic-operators-discrete-groups-and-von-neumann.pdf
 
 Exercise: Line tensor. What is a line tensor?
 A holomorphic section τ ∈ H⁰(Y_0, (Ω^1_{Y_0})^{⊗m} ⊗ B_ρ) whose "coefficient-line map" (dual of cotangent tensor factor → coefficient Hilbert space) has generic rank one. So the tensor is (locally) a holomorphic 1-form-line times a holomorphic coefficient vector; the coefficients vary inside a projective Hilbert line. Lemma (Plucker) produces a line tensor whose coefficient lines span an infinite-dimensional space: take an exterior power r of chained coefficients and antisymmetrize to get a decomposable rank-one entry inside a large tensor power.
 
 Exercise: Minimal rank s. What is minimized, and how is the minimal case characterized?
 Among all line tensors with infinite-dimensional coefficient span over finite orbifold covers, minimize the generic complex rank s of the coefficient-line map F: U° → PP(B_ρ). Rank zero would make F constant, giving a 1-dim. span; so 1 ≤ s ≤ ℓ. Proposition (Discrete Monodromy): after shrinking the finite-index subgroup Γ ≤ Q defining the cover, the isometry monodromy of F on its connected regular image-germ manifold Z acts properly, discretely, and effectively. Proof: build Z as a connected second-countable Hausdorff complex manifold of germs of rank-s plaques, use Myers–Steenrod/Manoussos to make the isometry group act properly, use Matveev–Troyanov and Tao no-small-subgroups to make it a Lie group, and show the identity component acts trivially on Z (otherwise minimality of s would be contradicted on a locally injective open set).
-Matveev–Troyanov 2017, The Myers–Steenrod theorem for Finsler manifolds of low regularity: https://arxiv.org/abs/1605.03850
+Matveev–Troyanov 2017, The Myers–Steenrod theorem for Finsler manifolds of low regularity: ./pdf/matveev-troyanov-2017-1605.03850-the-myers-steenrod-theorem-for-finsler-manifolds.pdf
 Manoussos 2010, On the action of the group of isometries on a locally compact metric space
-Tao 2014, Hilbert's Fifth Problem and Related Topics: https://terrytao.wordpress.com/wp-content/uploads/2014/11/gsm-153.pdf
+Tao 2014, Hilbert's Fifth Problem and Related Topics: ./pdf/tao-2014-hilbert-s-fifth-problem-and-related-topics.pdf
 
 Exercise: Compact fibres from mass. How compactify the I-orbit fibres of rank-s maps if the target is not compact?
 Lemma (Compact Fibres): let V be a smooth compact Kähler modification of the finite-cover source, and T a closed positive (1,1)-current on V that restricts on the smooth locus V° to a positive multiple of the transverse Kähler form f^*ω_Z from the local rank-s submersion f: V° → Z/I. The mass bound ∫_V T^s ∧ ω^{d−s} < ∞ follows from the pp-form calculus for truncated Monge–Ampère potentials (Boucksom). Coarea then shows almost every fibre has finite volume. El Mir's extension theorem: the integration current of such a finite-volume fibre extends as a positive closed current across the analytic complement; Siu's theorem: the Lelong superlevel sets of a closed positive current are analytic, so the support is compact analytic of pure dimension d − s. Those components meeting V° have fundamental group mapping into a finite stabilizer of I, so the Γ-reduction contracts them.
 El Mir 1984, Sur le prolongement des courants positifs fermés: https://doi.org/10.1007/BF02392374
 Siu 1974, Analyticity of sets associated to Lelong numbers: https://doi.org/10.1007/BF01389965
-Boucksom 2002, On the volume of a line bundle: https://arxiv.org/abs/math/0201031
+Boucksom 2002, On the volume of a line bundle: ./pdf/boucksom-2002-math0201031-on-the-volume-of-a-line-bundle.pdf
 
 Exercise: Minimality contradicts smaller s. How?
 Suppose the minimal line tensor has s < ℓ. Apply the minimality hypothesis (M) to Q_0 = Γ: get a connected finite cover S' → S with image Q' ⊆ Γ, and for every infinite quotient ψ: Q' → P an infinite image H, the Γ-reduction of ψ ∘ ν' has base dimension ≥ ℓ. Now ψ = im(Q') ⊆ I is an infinite quotient (since Γ's image in I is infinite), so the transverse Kähler current on V yields gdim(V, ρ) ≤ s (Lemma: Compact Fibres). That contradicts gdim ≥ ℓ. So s = ℓ.
 
 Exercise: Campana–Păun. How does s = ℓ finish Case A?
 Take a finite Galois orbifold cover dominating the minimal-rank cover. Tensor all deck-group translates of the descended line bundle: the result is a G-linearized line bundle M whose invariant metric has positive curvature, and which admits a nonzero map into a symmetric power of the orbifold cotangent tensor bundle. Equivariant descent gives a positive orbifold line bundle M_0 → a nonempty open subset with strictly positive curvature. A positive power of M_0 descends to an ordinary big line bundle A on Y (Boucksom volume criterion). Big line + Kähler ⇒ Moishezon ⇒ projective (Moishezon's theorem). On the Campana–Păun adapted Kawamata cover, π^*A injects into a tensor power of the adapted orbifold cotangent bundle; the Campana–Păun Theorem 7.11 (orbifold cotangent positivity) then forces K_Y + Δ big.
-Boucksom 2002, On the volume of a line bundle: https://arxiv.org/abs/math/0201031
+Boucksom 2002, On the volume of a line bundle: ./pdf/boucksom-2002-math0201031-on-the-volume-of-a-line-bundle.pdf
 Campana–Păun 2019, Foliations with positive slopes and birational stability of orbifold cotangent bundles: https://doi.org/10.1007/s10240-019-00105-w
 
 Exercise: Linear general-type. State the CCE linear general-type criterion.
 Theorem (Linear General-Type): if a compact Kähler manifold M has a generically large complex linear representation ρ with torsion-free image and connected simple semisimple Zariski closure, then M is of general type. Proof: CCE (2015) give a Shafarevich morphism sh_ρ: M → Sh_ρ(M) with normal projective target of general type; generic largeness forces the general fibre to be a point; the morphism is bimeromorphic; bimeromorphic invariance of Kodaira dimension finishes.
-CCE 2015, Linear representations of Kähler groups: https://arxiv.org/abs/1302.5016
+CCE 2015, Linear representations of Kähler groups: ./pdf/cce-2015-1302.5016-linear-representations-of-kahler-groups.pdf
 
 Exercise: Selberg's lemma. How does it give a torsion-free linear image?
 In Case B, an infinite complex linear image of Q → GL(V) is possible but the Zariski closure L is reductive-or-solvable. Pass to a finite-index subgroup of Q with connected L. Since Q is FAb, L has no infinite virtually solvable (or solvable) quotient; the semisimple quotient L/Rad(L) is nontrivial. Take a simple factor H of L_adj = (L/Rad(L))_ad. The projection Q → H(ℂ) has a Zariski-dense image. In the faithful adjoint representation, that image is a finitely generated linear group; Selberg's lemma gives a finite-index torsion-free subgroup. Pull back to Q, realize via the Realize-Finite-Index Lemma. The image in H(ℂ) stays Zariski dense (finite-index subgroup of a dense subgroup of the connected group H(ℂ) is still dense).
 Selberg 1960, On discontinuous groups in higher-dimensional symmetric spaces
-CCE 2015, Linear representations of Kähler groups: https://arxiv.org/abs/1302.5016
+CCE 2015, Linear representations of Kähler groups: ./pdf/cce-2015-1302.5016-linear-representations-of-kahler-groups.pdf
 
 Exercise: Meridian order m_D. How does it define the inertial boundary?
 Let p: X → Z be a dominant holomorphic map and ρ: π₁(X) → R a compatible homomorphism over a Zariski-open smooth fibration locus. For a prime divisor D ⊂ Z, let μ_D be a meridian loop around a general point of D (well-defined up to conjugacy). The order m_D = ord_R(ψ(μ_D)) is finite, because the preimage of D in X is a compact hypersurface whose transverse boundary maps trivially in R. Define Δ_Z = ∑_D (1 − 1/m_D) D. This is the "inertial boundary" and it is an invariant of the map and quotient, not of the model.
@@ -158,7 +158,7 @@ Exercise: klt pair. What is a klt pair (Z, Δ)?
 
 Exercise: Wang on tori. State the two Juanyong Wang theorems used.
 Theorem (Wang on Tori): (a) if Z is smooth compact Kähler, (Z, D) klt, and g: Z → A a fibration onto a complex torus, then κ(Z, K_Z + D) ≥ κ(F, K_F + D|_F) for a general smooth fibre F (subadditivity); (b) if κ(Z, K_Z + D) = 0, the Albanese morphism of Z is surjective with connected fibres. Both are Theorems A(II) and C of Wang 2021, valid over arbitrary complex tori (no projectivity).
-Juanyong Wang 2021, On the Iitaka conjecture C_{n,m} for Kähler fibre spaces: https://www.numdam.org/item/AFST_2021_6_30_4_813_0
+Juanyong Wang 2021, On the Iitaka conjecture C_{n,m} for Kähler fibre spaces: ./pdf/juanyong-wang-2021-on-the-iitaka-conjecture-c-n-m.pdf
 
 Exercise: Iitaka fibration. What is it?
 If κ(Z, L) = d ≥ 0, the m-th plurisection spaces H⁰(Z, mL) for large divisible m define meromorphic maps to projective space whose images eventually stabilize to a d-dimensional variety. The resulting fibration h: Z ⇢ W is the Iitaka fibration of L; it has connected general fibres, and K_Z + Δ restricted to a general fibre has Iitaka dimension 0. The torus descent theorem applies to the Iitaka fibration of L = K_Z + Δ_Z.
@@ -174,24 +174,24 @@ Apply Proposition (Minimal Base): Q = N/B_0 is infinite, FAb, has minimal-base Z
 
 Exercise: Kodaira-zero. State and prove the κ = 0 corollary.
 Corollary (Kodaira-Zero Abelianity): if X is smooth compact connected Kähler with κ(X) = 0, then π₁(X) is virtually abelian. Proof: Campana's Theorem 6.7 (κ = 0 ⇒ X special) reduces to the main theorem.
-Campana 2011, Orbifoldes géométriques spéciales et classification bimeromorphe des variétés kählériennes compactes: https://arxiv.org/abs/0705.0737
+Campana 2011, Orbifoldes géométriques spéciales et classification bimeromorphe des variétés kählériennes compactes: ./pdf/campana-2011-0705.0737-orbifoldes-geometriques-speciales-et-classification-bimeromo.pdf
 
 Exercise: Conjecture S. State the Conjecture S and Iitaka uniformization corollary.
 Corollary (Conjecture S and Iitaka Uniformization): if X is connected compact Kähler of complex dim n and either (i) X is special with γd(X) = n, or (ii) the ordinary universal cover of X is biholomorphic to ℂⁿ, then there is a connected finite étale cover X' → X bimeromorphic to a complex torus. Proof: the main theorem gives virtual abelianity; take the torsion-free abelian cover X'; π₁(X') → H_1(X', ℤ) is then an isomorphism; the Albanese map of X' is surjective with connected fibres; the group of a general Albanese fibre has trivial image in π₁(X'); maximality of ordinary Γ-dimension forces the general fibre to have dimension 0; so the Albanese is bimeromorphic. Assertion (ii) is Campana's implication (Conjecture S ⇒ the stated bimeromorphic Iitaka conclusion), from Remark A.4(2) of Claudon-Höring.
-Claudon-Höring 2013, Compact Kähler manifolds with compactifiable universal cover: https://doi.org/10.24033/bsmf.2651
+Claudon-Höring 2013, Compact Kähler manifolds with compactifiable universal cover: ./pdf/claudon-horing-2013-compact-kahler-manifolds-with-compactifiable-universal-cover.pdf
 
 Exercise: Holomorphic convexity. State the corollary and sketch it.
 Corollary (Special Shafarevich/Convexity): if X is smooth compact Kähler special, then the ordinary universal cover of X is holomorphically convex. Proof: G = π₁(X) is finitely generated and virtually abelian; take the finite-index abelian subgroup H; write H = ℤ^r ⊕ T; T finite. Construct a faithful finite-dimensional complex representation of H via powers of 2 on the ℤ-factors and roots of unity on the T-factors; induce to G. The induced rep is faithful because in the direct-sum realization indexed by left cosets of H, the kernel lies in H and acts faithfully there. Campana–Claudon–Eyssidieux's Kähler linear Shafarevich theorem (author's Corollary 5.9) gives holomorphic convexity of the ordinary universal cover.
-CCE 2015, Linear representations of Kähler groups: https://arxiv.org/abs/1302.5016
+CCE 2015, Linear representations of Kähler groups: ./pdf/cce-2015-1302.5016-linear-representations-of-kahler-groups.pdf
 
 Exercise: Compactifiable covers. State the two-part corollary.
 Corollary (Compactifiable Covers): (i) if X is connected normal compact Kähler and p: V → X a connected infinite étale Galois covering with deck group Γ, and V is a Zariski-open subset of a normal compact complex space, then Γ is virtually abelian. (ii) if X is a connected compact Kähler manifold and U the ordinary universal cover, and U is a Zariski-open subset of a normal compact Kähler space, then there is a connected finite étale X' → X whose Albanese α_{X'}: X' → A = Alb(X') is a locally trivial holomorphic fibre bundle with simply connected compact Kähler fibre F; writing q = dim_C A, U ≅ F × ℂ^q. Proof: (i) minimal-counterexample reduction of Claudon–Höring to a smooth special base; main theorem. (ii) apply (i); the Kähler compactification hypothesis is the Kähler analogue of Definition 2.3 in Claudon–Höring, and Theorem 1.5 gives the Albanese bundle on a connected finite étale cover X'. The pullback of the principal Aut(F)-bundle over A to ℂ^q is holomorphically trivial (Oka–Grauert), so U ≅ F × ℂ^q.
-Claudon-Höring 2013, Compact Kähler manifolds with compactifiable universal cover: https://doi.org/10.24033/bsmf.2651
+Claudon-Höring 2013, Compact Kähler manifolds with compactifiable universal cover: ./pdf/claudon-horing-2013-compact-kahler-manifolds-with-compactifiable-universal-cover.pdf
 
 Exercise: What wasn't assumed. What hypotheses does the proof not use?
 The proof needs no projectivity of X (Wang's theorems hold for arbitrary complex tori), no linearity of π₁(X) (Case A assumes no infinite linear image but does not require linearity), no maximality of ordinary Γ-dimension, no residual finiteness of π₁(X), and no prescribed value of κ(X). Compact Kähler is genuinely used—in Wang's subadditivity theorems, in Campana–Păun orbifold positivity, and in the Kähler Albanese story. The special sub-case κ(X) = 0 does not need anything beyond the main theorem plus Campana's essentially free κ = 0 ⇒ specialness.
 
 Exercise: Correctness bookkeeping. What is the role of the 2023 correction of Campana's Albanese theorem?
 Campana's 2004 paper claimed the Albanese map of a special manifold is surjective with connected fibres and has no multiple fibres. The multiple-fibre part had an error; the 2023 correction fixes it and requires a projective target for the multiple-fibre exclusion. The paper avoids that by not needing the multiple-fibre exclusion, using only surjectivity plus connectedness (which the correction preserves). The rest of the argument—especially the torus descent—depends on carefully tracking meridian orders in R = G/B_0 rather than assuming they vanish. This is why the descent section spends so much on the "actual inertial boundary" rather than a "canonical" one.
-Campana 2023, Albanese map of special manifolds: a correction: https://www.numdam.org/item/10.5802/aif.3563
-Juanyong Wang 2021, On the Iitaka conjecture C_{n,m} for Kähler fibre spaces: https://www.numdam.org/item/AFST_2021_6_30_4_813_0
+Campana 2023, Albanese map of special manifolds: a correction: ./pdf/campana-2023-albanese-map-of-special-manifolds-a-correction.pdf
+Juanyong Wang 2021, On the Iitaka conjecture C_{n,m} for Kähler fibre spaces: ./pdf/juanyong-wang-2021-on-the-iitaka-conjecture-c-n-m.pdf