From 96ca695e5ae2a31d092cfb826b9e8e0a6d9139a2 Mon Sep 17 00:00:00 2001 From: Luke Naylor <l.naylor@sms.ed.ac.uk> Date: Thu, 15 Jun 2023 23:58:33 +0100 Subject: [PATCH] Minor wording changes around main corrolary --- main.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/main.tex b/main.tex index 14d9cbb..f3e6e33 100644 --- a/main.tex +++ b/main.tex @@ -1403,8 +1403,8 @@ r_upper_bound_all_q = ( \let\originalDelta\Delta \renewcommand\Delta{{\psi^2}} The ranks of the pseudo-semistabilizers for $v$ are bounded above by the -maximum over $q\in [0, \chern_1^{\beta}(F)]\cap \frac{1}{n}\ZZ$ of the -expression in theorem \ref{thm:rmax_with_uniform_eps}. +maximum over $q\in [0, \chern_1^{\beta}(F)]$ of the expression in theorem +\ref{thm:rmax_with_uniform_eps}. Noticing that the expression is a maximum of two quadratic functions in $q$: \begin{equation*} f_1(q):=\sage{r_upper_bound1.rhs()} \qquad @@ -1429,7 +1429,7 @@ stated in the corollary. %% refinements using specific values of q and beta -This bound can be refined a bit more by considering restrictions from the +These bound can be refined a bit more by considering restrictions from the possible values that $r$ take. Furthermore, the proof of theorem \ref{thm:rmax_with_uniform_eps} uses the fact that, given an element of $\frac{1}{2n^2}\ZZ$, the closest non-equal element of -- GitLab