Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces

Antony Maciocia

Published 2012-02-21, updated 2013-06-04Version 2

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.