%0 Journal Article
%T Bridgeland Stability of Line Bundles on Surfaces
%A Daniele Arcara
%A Eric Miles
%J Mathematics
%D 2014
%I arXiv
%X We study the Bridgeland stability of line bundles on surfaces using Bridgeland stability conditions determined by divisors. We show that given a smooth projective surface $S$, a line bundle $L$ is always Bridgeland stable for those stability conditions if there are no curves $C\subseteq S$ of negative self-intersection. When a curve $C$ of negative self-intersection is present, $L$ is destabilized by $L(-C)$ for some stability conditions. We conjecture that line bundles of the form $L(-C)$ are the only objects that can destabilize $L$, and that torsion sheaves of the form $L(C)|_C$ are the only objects that can destabilize $L[1]$. We prove our conjecture in several cases, and in particular for Hirzebruch surfaces.
%U http://arxiv.org/abs/1401.6149v2