Minor tweaks

main.tex

@@ -383,7 +383,7 @@ The following facts can be deduced from the formulae for $\chern_i^{\alpha, \bet
 as well as the restrictions on $v$, when $\chern_0(v)=0$ and $\chern_1(v)>0$:
 
 
-\begin{minipage}{0.59\textwidth}
+\begin{minipage}{0.5\textwidth}
 \begin{itemize}
 	\item $V_v = \emptyset$
 	\item $\Theta_v$ is a vertical line at $\beta=\frac{D}{C}$
@@ -391,7 +391,7 @@ as well as the restrictions on $v$, when $\chern_0(v)=0$ and $\chern_1(v)>0$:
 \end{itemize}
 \end{minipage}
 \hfill
-\begin{minipage}{0.39\textwidth}
+\begin{minipage}{0.49\textwidth}
 	\sageplot[width=\textwidth]{Theta_v_plot}
 	%\caption{$\Delta(v)>0$}
 	%\label{fig:charact_curves_rank0}
@@ -1670,7 +1670,7 @@ lot when $m$ is small.
 from plots_and_expressions import main_theorem2_corollary
 \end{sagesilent}
 \begin{corollary}[Bound on $r$ \#3 on $\PP^2$ and Principally polarized abelian surfaces]
-\label{thm:rmax_with_eps1}
+\label{cor:rmax_with_eps1}
 	Suppose we are working over $\PP^2$ or a principally polarized abelian surface
 	(or any other surfaces with $m=1$ or $2$).
 	Let $v$ be a fixed Chern character, with $\frac{a_v}{n}=\beta\coloneqq\beta(v)$