From categories to geometry : stability conditions and Kleinian singularities

March 20, 2006    11:00-12:00
Speaker: Tom Bridgeland (University of Edinburgh)

Abstract:

Let f : Y --> X be the minimal resolution of a Kleinian surface singularity. Let D \subset D^b Coh(Y) be the full subcategory of the derived category of Y consisting of objects E satisfying R f_* (E) = 0. Let h^{reg} denote the regular part of the Cartan subalgebra of the corresponding complex Lie algebra. I shall try to explain how h^{reg} arises as the space of stability conditions on the category D.