From 015e6d74a6a51d742c03977bd62a42157706ad43 Mon Sep 17 00:00:00 2001 From: Luke Naylor <l.naylor@sms.ed.ac.uk> Date: Wed, 13 Sep 2023 21:58:32 +0100 Subject: [PATCH] Extend main lemma to rank 0 --- main.tex | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/main.tex b/main.tex index 3749d16..8550862 100644 --- a/main.tex +++ b/main.tex @@ -505,7 +505,7 @@ semistabilizing sequence. \begin{lemma}[Numerical tests for left-wall pseudo-semistabilizers] \label{lem:pseudo_wall_numerical_tests} Let $v$ and $u$ be Chern characters with $\Delta(v), -\Delta(u)\geq 0$, and $v$ has positive rank. Let $P$ be a point on $\Theta_v^-$. +\Delta(u)\geq 0$, and $v$ has non-negative rank. Let $P$ be a point on $\Theta_v^-$. \noindent The following conditions: @@ -613,6 +613,8 @@ Therefore, it's also a pseudo-semistabilizer further along the circle at $Q$ Finally, consequence 4 along with $P$ being to the left of $V_u$ implies $\nu_P(u) > 0$ giving supposition b. +The case with rank 0 can be handled the same way. + \end{proof} \section{The Problem: Finding Pseudo-walls} -- GitLab