Add some content for notable stabs

main.tex

@@ -290,5 +290,50 @@
 	}
 \end{frame}
 
+\begin{frame}{Notable Stability Conditions on Plane}
+	\begin{columns}[t,onlytextwidth] % align columns
+		\begin{column}{.49\linewidth}
+			When $\beta = \mu(E)$ \\
+			$\nu_{\alpha, \beta}(E) = + \infty$ so can only be destabilized by
+			$F \hookrightarrow E$ with $\nu_{\alpha, \beta}(F) = + \infty$ too
+			($\beta = \mu(F)$)
+		\end{column}%
+		\hfill%
+		\begin{column}{.49\linewidth}
+			\begin{align*}
+				\nu_{\alpha, -n}(E) &=
+				\frac{
+					\chern_2(E\otimes L^n)
+					{\color{gray}
+					- \frac{\alpha^2}{2} \rank(E)
+					}
+				}{
+					{\color{gray}
+					(\chern_1(E) +
+					}
+					n \rank(E)
+					{\color{gray}
+					)
+					}
+				}
+			\end{align*}
+			
+			\begin{tcolorbox}[title=Gieseker Stability]
+				E stable when red. Hilb. poly.
+				\[
+					p_E(n) = \frac{\chern_2(E\otimes L^n)}{\rank(E)}
+				\]
+				not overtaken by that of any \\
+				$0 \not= F \hookrightarrow E$, for large $n$. \\
+				{\color{gray}
+				(equiv. to lexic. comparison between poly. coeffs)
+				}
+			\end{tcolorbox}
+		\end{column}
+	\end{columns}
+\end{frame}
+
+\section{Walls}
+% walls, make the explanation about fixing a Chern character
 
 \end{document}