DMM Seminar

Speaker: Timothy Logvinenko (Warwick)
Title: Derived Reid's recipe for threefold singularities (Part I)
Date (JST): Mon, Nov 14, 2011, 15:30 - 17:00
Place: Seminar Room A
Abstract: Part I:

I begin with an overview of the classical McKay correspondence between irreducible representations of finite G \subset SL_2(C) and irreducible exceptional curves on the minimal resolution Y of C^2/G.
I then explain how this correspondence was realised as a natural K-theory isomorphism by Gonzales-Sprinberg and Verdier, and then generalised to the famous derived category equivalence by Bridgeland, King and Reid (BKR), which holds for all finite subgroups G of SL_3(C), as well as SL_2(C).

I then explain how we can extract from BKR equivalence a more geometrical correspondence which we call "derived Reid's recipe": to every representation of G it assigns a subvariety of the exceptional set of Y. In dimension 2 this gives precisely the classical McKay correspondence discussed above. In dimension 3, this gives a new, previously unknown correspondence. For an abelian G we prove it to be governed completely by an old toric geometry calculation known as "Reid's recipe"