From 79a9895e5eb5cadc19737192524a1202868114c7 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 19 Jul 2023 17:00:18 +0100
Subject: [PATCH] Add ref in intro to def of semistabilizer

---
 main.tex | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/main.tex b/main.tex
index 73f918c..11511ff 100644
--- a/main.tex
+++ b/main.tex
@@ -116,10 +116,10 @@ showed that there are infinitely many walls.
 
 This dichotomy does not only hold for real walls, realised by actual objects in
 $\bddderived(X)$, but also for pseudowalls. Here pseudowalls are defined as
-`potential' walls, induced by hypothetical Chern characters of destabilizers
+`potential' walls, induced by hypothetical Chern characters of semistabilizers
 which satisfy certain numerical conditions which would be satisfied by any real
 destabilizer, regardless of whether they are realised by actual semistabilizers
-in $\bddderived(X)$.
+in $\bddderived(X)$ (dfn \ref{dfn:pseudo-semistabilizer}).
 
 Since real walls are a subset of pseudowalls, the irrational $\beta_{-}$ case
 follows immediately from the corresponding case for real walls.
@@ -159,6 +159,7 @@ working over one of the following two surfaces: principally polarized abelian
 surfaces and $\PP^2$.
 
 \begin{dfn}[Pseudo-semistabilizers]
+\label{dfn:pseudo-semistabilizer}
 % NOTE: SURFACE SPECIALIZATION
 	Given a Chern Character $v$, and a given stability
 	condition $\sigma_{\alpha,\beta}$,
-- 
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