Speaker: Yujiro Kawamata (University of Tokyo)

Time: 14:00-15:00, April 29th, 2015

Venue: Room 77201, Jingchunyuan Garden, BICMR

Abstract: Let G be a nite subgroup of SL(2,C). McKay found a correspondence between(1) the quiver consisting of irreducible representations of G that is denedusing the tensor product with the natural representation and(2) the extended Dynkin diagram of exceptional curves on the minimal resolution Y of the quotient space . This phenomena is understood as an equivalence of derived categories betweenthe quotient stack and Y . Such equivalence is extended to the case of a nite subgroup of SL(3,C) byBridgeland-King-Reid. In this talk we consider the case where G is a nite abelian subgroup of GL(n,C). The quotient space is a toric variety and there exists a toric terminalization Y ! X. We explain how to use the toric minimal model program to prove the following theorem; there exists a semi-orthogonal decomposition of the derived categoryof the quotient stack into the derived category of Y and otherderived categories of smaller dimensional quotient stacks.