Gluing stability conditions

Details Gluing stability conditions Gluing stability conditions

2009-02-02

arxiv.org/abs/0902.0323v3

Mathematics

Algebraic Geometry

31 pages, v2: a minor mistake corrected, v3: added the identification of the Riemann surface appearing in the description of o

Scientific paper

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 ${\mathbb{Z}}_2$-equivariant sheaves associated with ramified double coverings of ${\mathbb{P}}^3$. Also, we study the stability space for the derived category of ${\mathbb{Z}}_2$-equivariant coherent sheaves on a smooth curve $X$, associated with a degree 2 map $X\to Y$, where $Y$ is another smooth curve. In the case when the genus of $Y$ is $\geq 1$ we give a complete description of the stability space.

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