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Derived Reid's recipe for abelian subgroups of SL^3©

Timothy Logvinenko
(Cardiff University)
Onsdag, 11 september, 2013, at 16:30-17:30, in Aud. D3 (1531-215)

The classical McKay correspondence is a 1-1 correspondence between non-trivial irreducible representations of a finite subgroup G of SL^2(C) and irreducible divisors on the minimal resolution Y of C^2/G.

In this talk I first introduce, explain and illustrate this classical correspondence. Then I describe joint work with Sabin Cautis and Alastair Craw in which we generalise it to dimension three using the famous Bridgeland-King-Reid derived equivalence. Specifically, we show a natural way to extract from this equivalence a correspondence between irreducible representations of G ⊂ SL^3(C) and exceptional subvarieties of Y = G-Hilb(C^3). The same method applied to G ⊂ SL^2(C) produces the classical McKay.

Organiseret af: QGM
Kontaktperson: Sergey Arkhipov