The Western Algebraic Geometry Seminar


Speaker: Dan Abramovich
Title: Valuative criteria for stable complexes
Motivated by ideas from Physics, Tom Bridgeland defined a notion of a
stability condition on the derived category of coherent sheaves on a
projective manifold. This notion generalizes the notion of stability
of vector bundles on curves. Bridgeland went on to prove that the
collection of all stability conditions on the derived category of a
projective manifold forms a complex manifold - one which is of much
interest for mathematical physicists. A different natural mathematical
question is the study of moduli spaces of stable objects uner a given
stability condition.

I will review Bridgeland's stability conditions, and discuss joint
work with Alexander Polishchuk proving valuative criteria for
properness and separation for the moduli of semistable objects under a
noetherian stability condition.