From 8c79d043885a98a34fbe9ff1d2b839be9d7a1f51 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 19 Apr 2023 18:22:54 +0100
Subject: [PATCH] =?UTF-8?q?Syntax=20sugar=20up=20bg=20forms=20with=20?=
 =?UTF-8?q?=CE=94?=
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---
 main.tex | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/main.tex b/main.tex
index c560ce7..63d5c71 100644
--- a/main.tex
+++ b/main.tex
@@ -154,6 +154,8 @@ $\chern(E) = (r,c,d)$ of some semistabilizer $E$.
 
 	v = Chern_Char(*var("R C D", domain="real"))
 	u = Chern_Char(*var("r c d", domain="real"))
+
+	Δ = lambda v: v.Q_tilt()
 \end{sagesilent}
 
 Recall [ref] that $\chern_1^{\beta_{-}}$ has fixed bounds in terms of
@@ -185,7 +187,8 @@ and we shall be varying $\chern_0(E) = r$ to see when certain inequalities fail.
 This condition expressed in terms of $R,C,D,r,c,d$ looks as follows:
 
 \begin{sagesilent}
-	bgmlv1 = - u.Q_tilt() - (v-u).Q_tilt() + v.Q_tilt()
+	# First Bogomolov-Gieseker form expression that must be non-negative:
+	bgmlv1 = Δ(v) - Δ(u) - Δ(v-u)
 \end{sagesilent}
 
 \begin{equation}
-- 
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