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 ${\widehat{sl}}_m$.

14 pages, published version

References in corpus (2)

• Hilbert schemes, Hecke algebras and the Calogero-Sutherland system
• Homogeneous components in the moduli space of sheaves and Virasoro characters