Adjust problems section to more general surface

main.tex

@@ -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}