Bridgeland Stability of Line Bundles on Surfaces

Understand

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 $L[1]$.