diff --git a/main.tex b/main.tex
index a929a45ec2355e9fb1fe85bd1b6ba023eae4027c..8205f8693e8f18c4f8d15fa06bf36549f1e2da95 100644
--- a/main.tex
+++ b/main.tex
@@ -204,9 +204,10 @@ location of the pseudo-wall where $u$ pseudo-semistabilizes $v$.
 %TODO ref forwards
 
 Commenting on the geometry of the hyperbola, it always has left and right
-branches, or degenerates to 2 lines. This is a consequence of $\Delta(v)\geq 0$.
-Furthermore the assymptotes are angled at $\pm 45^\circ$, crossing through the
-base of the first characteristic curve $\chern_1^{\alpha,\beta}=0$ (vertical line).
+branches (as opposed to up and down), or degenerates to 2 lines. This is a
+consequence of $\Delta(v)\geq 0$. Furthermore the assymptotes are angled at $\pm
+45^\circ$, crossing through the base of the first characteristic curve
+$\chern_1^{\alpha,\beta}=0$ (vertical line).