From 98713f85912f8704c0f51f90973cd98a485c705d Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Mon, 12 Aug 2024 16:20:47 +0100
Subject: [PATCH] Tweak wording to reduce text overflow into margin.
---
tex/bounds-on-semistabilisers.tex | 2 +-
tex/setting-and-problems.tex | 4 ++--
2 files changed, 3 insertions(+), 3 deletions(-)
diff --git a/tex/bounds-on-semistabilisers.tex b/tex/bounds-on-semistabilisers.tex
index 59030e9..06fd0f6 100644
--- a/tex/bounds-on-semistabilisers.tex
+++ b/tex/bounds-on-semistabilisers.tex
@@ -979,7 +979,7 @@ Next, we seek to find a larger $\epsilon$ to use in place of $\epsilon_v$ in the
proof of Theorem \ref{thm:rmax_with_uniform_eps}:
\begin{lemmadfn}[%
- Finding a better alternative to $\epsilon_v$:
+ A better alternative to $\epsilon_v$:
$\epsilon_{v,q}$
]
\label{lemdfn:epsilon_q}
diff --git a/tex/setting-and-problems.tex b/tex/setting-and-problems.tex
index 9a6cf08..d9c8a3f 100644
--- a/tex/setting-and-problems.tex
+++ b/tex/setting-and-problems.tex
@@ -167,7 +167,7 @@ are equivalent to the following more numerical conditions:
\begin{proof}
First, consider the case where $\chern_0(v)>0$.
-Let $u,v$ be Chern characters with
+Let $u,v$ be Chern characters such that
$\Delta(u),\Delta(v) \geq 0$, and $v$ has positive rank.
For the forwards implication, assume that the suppositions of the Lemma are
@@ -461,7 +461,7 @@ problem using Lemma \ref{lem:pseudo_wall_numerical_tests}.
\begin{proof}
Consider the context of $v$ being a Chern character with non-negative rank
- (and $\chern_1(v)>0$ if rank 0)
+ (and with $\chern_1(v)>0$ if rank 0)
and
$\Delta \geq 0$, and $u$ being a Chern character with $\Delta(u) \geq 0$.
Lemma \ref{lem:pseudo_wall_numerical_tests} gives that the remaining
--
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