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Commit d5057731 authored by Luke Naylor's avatar Luke Naylor
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Adjust problems section to more general surface

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......@@ -218,7 +218,6 @@ $d \in \frac{1}{\lcm(m,2)}\ZZ$.
% cover that being a pseudo-semistabilizer somewhere implies also on whole circle
\begin{lemma}[Sanity check for Pseudo-semistabilizers]
% NOTE: SURFACE SPECIALIZATION
Given a stability
condition $\sigma_{\alpha,\beta}$,
if $E\hookrightarrow F\twoheadrightarrow G$ is a semistabilizing sequence in
......@@ -594,7 +593,7 @@ problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
\label{lem:num_test_prob1}
Given a Chern character $v$ with positive rank and $\Delta(v) \geq 0$,
and a choice of point $P$ on $\Theta_v^-$.
Solutions $u=(r,c\ell,d\frac{1}{2}\ell^2)$
Solutions $u=(r,c\ell,\frac{e}{\lcm(m,2)}\ell^2)$
to problem \ref{problem:problem-statement-1}.
Are precisely given by integers $r,c,d$ satisfying the following conditions:
\begin{enumerate}
......@@ -604,7 +603,7 @@ problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
\label{item:bgmlvu:lem:num_test_prob1}
\item $\Delta(v-u) \geq 0$
\label{item:bgmlvv-u:lem:num_test_prob1}
\item $\mu(u)=\frac{c}{r}<\mu(v)$
\item $\mu(u)<\mu(v)$
\item $0\leq\chern_1^{\beta(P)}(u)\leq\chern_1^{\beta(P)}(v)$
\label{item:chern1bound:lem:num_test_prob1}
\item $\chern_2^{P}(u)>0$
......@@ -628,9 +627,9 @@ problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
\label{cor:num_test_prob2}
Given a Chern character $v$ with positive rank and $\Delta(v) \geq 0$,
such that $\beta_{-}\coloneqq\beta_{-}(v) \in \QQ$.
Solutions $u=(r,c\ell,d\frac{1}{2}\ell^2)$
Solutions $u=(r,c\ell,\frac{e}{\lcm(m,2)}\ell^2)$
to problem \ref{problem:problem-statement-2}.
Are precisely given by integers $r,c,d$ satisfying the following conditions:
Are precisely given by integers $r,c,e$ satisfying the following conditions:
\begin{enumerate}
\item $r > 0$
\label{item:rankpos:lem:num_test_prob2}
......@@ -638,7 +637,7 @@ problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
\label{item:bgmlvu:lem:num_test_prob2}
\item $\Delta(v-u) \geq 0$
\label{item:bgmlvv-u:lem:num_test_prob2}
\item $\mu(u)=\frac{c}{r}<\mu(v)$
\item $\mu(u)<\mu(v)$
\label{item:mubound:lem:num_test_prob2}
\item $0\leq\chern_1^{\beta_{-}}(u)\leq\chern_1^{\beta_{-}}(v)$
\label{item:chern1bound:lem:num_test_prob2}
......
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