Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes
Abstract
In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the numbers of quasihomogeneous components in a moduli space of sheaves on the projective plane. The answer is given in terms of characters of the affine Lie algebra $\hat{sl}_m$.
 Publication:

arXiv eprints
 Pub Date:
 June 2012
 arXiv:
 arXiv:1206.5640
 Bibcode:
 2012arXiv1206.5640B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics
 EPrint:
 14 pages, published version