Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces

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.

18 pages, 2 figures. A lot of tidying up following referee's comments especially in section 3. To appear in Asian J. Math

References in corpus (4)

• Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces
• Reider's Theorem and Thaddeus Pairs Revisited
• Some moduli spaces of Bridgeland's stability conditions
• Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces

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