|Speaker:||Yukari Ito (Nagoya U.)|
|Title:||McKay correspondence via G-Hilbert schemes|
|Date (JST):||Mon, Feb 20, 2012, 11:00 - 15:00|
|Place:||Seminar Room B|
In this part, I will explain 2-dimesional McKay correspondence and construction of G-Hilbert scheme. The original McKay correspondence was observed by John McKay in representation theory and explained in terms of algebraic geometry by Gonzalez-Sprinberg and Verdier later.
This correspondence is based on the existence of the minimal resolution of 2-dimensional singulariteis and generalized it more general quotient singularities as Special McKay correspondence.
Later, Ito and Nakamura gave a new construction of the minimal resolution of a quotient singularity for finite subgroup G in SL(2,C), so called G-Hilbert scheme, and it has many information about the representaions of the group G.
In this part, I want to generalize the results in part I to 3-dimensional case.
For a generalized McKay correspondence, we need a crepant resolution and there are several ways to explain the correspondece between Geometry of the resolution and Algebra of the group.
It is easy to see many exmaples for abelian subgroups, but I would like to introduce resent result related with G-Hilbert schemes for non-abelian subgroups in SL(3,C) with Akira Ishii and Alvaro Nolla de Celis (arXiv:1108.2310).