Stability Conditions II

Abstract: In moduli problems, one usually needs to impose some sort of "stability" on the objects being classified in order to have well-behaved moduli spaces. Generalizing this concept, in 2007, Bridgeland defined "stability conditions" on a triangulated category and proved that, under some mild conditions, the set of stability conditions can be given the structure of a complex manifold. In this three-part series, we shall explore this construction. We shall also give examples of stability conditions when the underlying triangulated category is the derived category of coherent sheaves on a smooth, projective variety.

Reference: Bridgeland, Tom. Stability conditions on triangulated categories. Ann. of Math. (2) 166 (2007), no.2, 317–345.

algebraic geometry

Audience: researchers in the discipline

ODTU-Bilkent Algebraic Geometry Seminars