On the McKay correspondences for the Hilbert scheme of points on the affine plane

2004/10/11 by Samuel Boissiere, Boissiere, Samuel
Mathematics · #14C05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C05

paper · pdf · doi:10.48550/arxiv.math/0410281

15 pages

arxiv created 2004/10/11 · arxiv updated 2009/12/01

Abstract

The quotient of a finite-dimensional vector space by the action of a finite subgroup of automorphisms is usually a singular variety. Under appropriate assumptions, the McKay correspondence relates the geometry of nice resolutions of singularities and the representations of the group. For the Hilbert scheme of points on the affine plane, we study how different correspondences (McKay, dual McKay and multiplicative McKay) are related to each other.

Related

• Hilbert schemes of points via McKay correspondences
• Towards the multiplicative behavior of the K-theoretical McKay correspondence
• McKay correspondence and Hilbert schemes in dimension three
• Hilbert schemes, wreath products, and the McKay correspondence
• The multiplicative structure of the K-theoretical McKay correspondence for the Hilbert scheme of points in the complex plane