diff --git a/main.tex b/main.tex index 73f918c213f79459a91caf53050720f17a68525e..11511ff11bfd67b40e56ac82a85bfea4027cb6c4 100644 --- a/main.tex +++ b/main.tex @@ -116,10 +116,10 @@ showed that there are infinitely many walls. This dichotomy does not only hold for real walls, realised by actual objects in $\bddderived(X)$, but also for pseudowalls. Here pseudowalls are defined as -`potential' walls, induced by hypothetical Chern characters of destabilizers +`potential' walls, induced by hypothetical Chern characters of semistabilizers which satisfy certain numerical conditions which would be satisfied by any real destabilizer, regardless of whether they are realised by actual semistabilizers -in $\bddderived(X)$. +in $\bddderived(X)$ (dfn \ref{dfn:pseudo-semistabilizer}). Since real walls are a subset of pseudowalls, the irrational $\beta_{-}$ case follows immediately from the corresponding case for real walls. @@ -159,6 +159,7 @@ working over one of the following two surfaces: principally polarized abelian surfaces and $\PP^2$. \begin{dfn}[Pseudo-semistabilizers] +\label{dfn:pseudo-semistabilizer} % NOTE: SURFACE SPECIALIZATION Given a Chern Character $v$, and a given stability condition $\sigma_{\alpha,\beta}$,