Gluing stability conditions

Abstract

We define and study a gluing procedure for Bridgeland stability conditions in the situation when a triangulated category has a semiorthogonal decomposition. As an application, we construct stability conditions on the derived categories of Z{double-struck}2-equivariant sheaves associated with ramified double coverings of P{double-struck}3. Also, we study the stability space for the derived category of Z{double-struck}2-equivariant coherent sheaves on a smooth curve X, associated with a degree 2 map X → Y, where Y is another smooth curve. In the case when the genus of Y is ≥ 1 we give a complete description of the stability space. © 2010 International Press.