diff --git a/main.tex b/main.tex index 504b0fe98e3378801b4c021534c61b4f1e9a8338..e9975ab630b93b436d9f261a2f21816d80eadc9b 100644 --- a/main.tex +++ b/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 $\frac{a_v}{n}=\beta\coloneqq\beta(v)$