Seminario Dottorato: On some aspects of McKay Correspondence and its applications

Wednesday 16 December 2009 - Luca Scala

ARGOMENTI: Seminars Ph.D. Program

Wednesday 16 December 2009 h. 15:00, room 2BC/60
Luca Scala (University of Chicago)
"On some aspects of McKay Correspondence and its applications"

When we quotient C2 by a finite subgroup G of SL(2,C), and we take a minimal resolution Y of the kleinian singularity C2 /G, then Y is a crepant resolution and the exceptional locus consists of a bunch of curves, whose dual graph is a Dynkin diagram of the kind An, Dn, E6, E7, E8. In the eighties, McKay noticed that the Dynkin diagrams arising from resolutions of kleinian singularities are in tight connection with the representations of G. In the first and introductory part of the talk, we will explain the McKay correspondence and its key generalization by means of K-theory, due to Gonzalez-Sprinberg and Verdier. The latter point of view opens the way to the modern derived McKay correspondence, due to Bridgeland-King-Reid. We will then see some applications of the BKR theorem to the geometry of Hilbert schemes of points, due to Haiman, and some other consequences related to the cohomology of tautological bundles.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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