Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces

TL;DR

This paper establishes criteria for the existence and finiteness of walls in Bridgeland stability conditions on projective surfaces, providing tools to locate or exclude walls in specific cases.

Contribution

It introduces explicit conditions to determine the boundedness and finiteness of walls, enhancing understanding of stability conditions on surfaces.

Findings

Walls are bounded in certain stability condition planes.

Conditions for the global finiteness of walls are derived.

Examples demonstrate how to locate or exclude walls explicitly.

Abstract

We derive constraints on the existence of walls for Bridgeland stability conditions for general projective surfaces. We show that in suitable planes of stability conditions the walls are bounded and derive conditions for when the number of walls is globally finite. In examples, we show how to use the explicit conditions to locate walls and sometimes to show that there are no walls at all.