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

Timothy Logvinenko
(Cardiff University)
Seminar
Wednesday, 11 September, 2013, at 16:30-17:30, in Aud. D3 (1531-215)
Abstract:

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 $G \subset SL^3(C)$ and exceptional subvarieties of $Y = G-Hilb(C^3)$. The same method applied to $G \subset SL^2(C)$ produces the classical McKay.

Organised by: QGM
Contact person: Sergey Arkhipov