diff --git a/cohomological_transfer_equivariant_v2.txt b/cohomological_transfer_equivariant_v2.txt
index 4328f14..bfc8c3f 100644
--- a/cohomological_transfer_equivariant_v2.txt
+++ b/cohomological_transfer_equivariant_v2.txt
@@ -39,29 +39,17 @@
 \DeclareMathOperator{\codim}{codim}
 \newcommand{\hol}[1]{\mathcal O_{#1}}
 
-\title[Cohomological transfer and anticanonical sections]{Cohomological transfer and equivariant anticanonical sections\\[2pt]\large A reader's edition for a first mathematical audience}
+\title[Cohomological transfer and anticanonical sections]{Cohomological transfer and equivariant anticanonical sections}
 
 
 \begin{document}
 \begin{abstract}
-Let $X$ be a smooth projective complex variety, and suppose its anticanonical line bundle $L=-K_X$ admits a Hermitian metric whose Chern curvature is nonnegative: in a word, $L$ is \emph{smoothly semipositive}. We prove that $X$ then has a nonzero section of some positive multiple $mL$. We prove more. If an algebraic torus $T$ acts on $X$ and a section of $M+iL$ exists for unbounded positive integers $i$, invariant under the torus and with one fixed error $M$ whose inverse $-M$ is pseudoeffective, then an invariant section of a positive untwisted power $mL$ exists. The number $m$ may depend on the data; the paper does not produce a uniform $m$. The engine is a field of ratios of invariant sections. The engine has three consequences: natural invariant nonvanishing under a nonzero Euler characteristic; ordinary nonvanishing without that hypothesis, via compact monodromy and a finite norm; and exact source characters from a one-parameter action. Several independent routes to the same conclusion (Iitaka, harmonic restriction, alteration, multiplier ideal, stabilized direct image) are given so that the reader can see how the same obstructions are handled in different regularity regimes. This edition is an expanded and reorganised presentation of the original paper; it does not change the mathematics and it deliberately spells out the ideas that the original assumed its audience could supply.
+Let $X$ be a smooth projective complex variety, and suppose its anticanonical line bundle $L=-K_X$ admits a Hermitian metric whose Chern curvature is nonnegative: in a word, $L$ is \emph{smoothly semipositive}. We prove that $X$ then has a nonzero section of some positive multiple $mL$. We prove more. If an algebraic torus $T$ acts on $X$ and a section of $M+iL$ exists for unbounded positive integers $i$, invariant under the torus and with one fixed error $M$ whose inverse $-M$ is pseudoeffective, then an invariant section of a positive untwisted power $mL$ exists. The number $m$ may depend on the data; the paper does not produce a uniform $m$. The engine is a field of ratios of invariant sections. The engine has three consequences: natural invariant nonvanishing under a nonzero Euler characteristic; ordinary nonvanishing without that hypothesis, via compact monodromy and a finite norm; and exact source characters from a one-parameter action. Several independent routes to the same conclusion (Iitaka, harmonic restriction, alteration, multiplier ideal, stabilized direct image) are given so that the reader can see how the same obstructions are handled in different regularity regimes. 
 \end{abstract}
 \maketitle
 \tableofcontents
 
-\section*{How to read this paper}\addcontentsline{toc}{section}{How to read this paper}
 
-This paper proves one small but stubborn-sounding thing: on a projectivised curved space $X$ of a certain positive type, some positive power of the anticanonical bundle has a nonzero section. Read on for what that sentence means and why it is not obvious. Read the rest for a proof.
-
-There are three audiences for the body. The first is a graduate student in algebraic or complex geometry who wants to understand the original paper without first learning every piece of its analytic apparatus. The second is a reader with a strong undergraduate background who wants the ideas first and the machinery second. The third is a curious high-school reader. Sections~\ref{sec:question}, \ref{sec:vocab}, and the beginning of every later section are aimed at the third audience: they explain, in words first, what is about to be proved. Everything after the words is written at the first audience's level. A student may skim the proofs and still follow the narrative; a researcher may skip the narrative and still find the proofs.
-
-The method has an unusual feature worth flagging at the start. Every construction in this paper is presented in two registers: the \emph{plain form} and the \emph{technical form}. The plain form takes one to five sentences and can be read without stopping. The technical form is the actual proof. The two forms refer to the same object; if you cannot follow the technical form, the plain form tells you what the object is for.
-
-A second feature is that we do not chase a \emph{uniform} exponent. Some power of $mL$ will be produced; the paper does not say which. This is typical in the subject and is not a defect: the exponent can jump when a section has common powers taken on compact factors or when a finite norm is formed.
-
-A third feature is that the paper deliberately offers several routes to its main corollary. The routes are not logically necessary; one route would prove the result. They are given because at different points in the argument different obstructions dominate, and different analytic theorems handle each obstruction. A reader who wants to see how a harmonic argument attacks a problem, here it is. A reader who wants to see how an algebraic argument attacks the same problem, here it is.
-
-A last word before the mathematics. If a sentence below says \emph{semipositive}, a high-school reader can think: the curvature is nonnegative everywhere. If a sentence says \emph{pseudoeffective}, a reader can think: its negative neighbour has nonnegative degree on every curve; the class lies in the closure of effective curves. If a sentence says \emph{invariant}, a reader can think: the torus action fixes the section, not just the line.
 
 \section{The question, and the shape of the answer}\label{sec:question}