diff --git a/main.tex b/main.tex index edf57c801e5d7e1beb7f93e3801cdfb28878ed2f..f1c8d2efa4679bb0b88058a285c700b1fd17d2ed 100644 --- a/main.tex +++ b/main.tex @@ -560,8 +560,7 @@ are trying to solve for. \begin{problem}[sufficiently large `left' pseudo-walls] \label{problem:problem-statement-1} -Fix a Chern character $v$ with positive rank, $\Delta(v) \geq 0$, -and $\beta_{-}(v) \in \QQ$. +Fix a Chern character $v$ with positive rank, and $\Delta(v) \geq 0$. The goal is to find all pseudo-semistabilizers $u$ which give circular pseudo-walls containing some fixed point $P\in\Theta_v^-$. @@ -598,13 +597,18 @@ $v-u$ for each solution $u$ of the problem. Fix a Chern character $v$ with positive rank, $\Delta(v) \geq 0$, and $\beta_{-}(v) \in \QQ$. -The goal is to find all solutions $u=(r,c\ell,d\ell^2)$ +The goal is to find all solutions $u$ to problem \ref{problem:problem-statement-1} with the choice $P=(\beta_{-},0)$. - -This will give all circular pseudo-walls left of $V_v$. \end{problem} +This is a specialization of problem (\ref{problem:problem-statement-1}) +which will give all circular pseudo-walls left of $V_v$. +This is because all circular walls left of $V_v$ intersect $\Theta_v^-$. +The $\beta_{-}(v) \in \QQ$ condition is to ensure that there are finitely many +solutions. As mentioned in the introduction (\ref{sec:intro}), this is known, +however this will also be proved again in passing in this article. + \section{B.Schmidt's Solutions to the Problems}