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Commit fde6e979 authored by Luke Naylor's avatar Luke Naylor
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Add justificatiosn for problem 2

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......@@ -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}
......
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