From e11d499de387aefcbd6a7bb026c8b385ec8cfc70 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 19 Apr 2023 17:09:11 +0100
Subject: [PATCH] Antony feedback: change m to q since it is rational, not
integer
---
main.tex | 10 +++++-----
1 file changed, 5 insertions(+), 5 deletions(-)
diff --git a/main.tex b/main.tex
index 4b2332a..406c5ca 100644
--- a/main.tex
+++ b/main.tex
@@ -163,19 +163,19 @@ $\chern(F)$, and so we can write:
beta_min = var("beta", domain="real")
c_lower_bound = -(ts(beta=beta_min).rank(u)/ts().alpha).expand() + c
- var("m", domain="real")
- c_val = c_lower_bound + m
+ var("q", domain="real")
+ c_val = c_lower_bound + q
\end{sagesilent}
\begin{equation}
\label{eqn-cintermsofm}
c=\chern_1(E) = \sage{c_val}
- \qquad 0 \leq m \leq \chern_1^{\beta_{-}}(F)
+ \qquad 0 \leq q \leq \chern_1^{\beta_{-}}(F)
\end{equation}
Furthermore, $\chern_1 \in \ZZ$ so we only need to consider
-$m \in \frac{1}{n} \ZZ \cap [0, \chern_1^{\beta_{-}}(F)]$.
-For the next subsections, we consider $m$ to be fixed with one of these values,
+$q \in \frac{1}{n} \ZZ \cap [0, \chern_1^{\beta_{-}}(F)]$.
+For the next subsections, we consider $q$ to be fixed with one of these values,
and we shall be varying $\chern_0(E) = r$ to see when certain inequalities fail.
--
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