Homogeneous components in the moduli space of sheaves and Virasoro characters

Abstract

The moduli space $\mathcal{M}(r,n)$ of framed torsion free sheaves on the projective plane with rank $r$ and second Chern class equal to $n$ has the natural action of the $(r+2)$-dimensional torus. In this paper, we look at the fixed point set of different one-dimensional subtori in this torus. We prove that in the homogeneous case the generating series of the numbers of the irreducible components has a beautiful decomposition into an infinite product. In the case of odd $r$ these infinite products coincide with certain Virasoro characters. We also propose a conjecture in a general quasihomogeneous case.

Published version, 19 pages

References in corpus (2)

• Heisenberg action in the equivariant K-theory of Hilbert schemes via Shuffle Algebra
• The moduli space of sheaves and the generalization of MacMahon's formula

Cited by in corpus (1)

• Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes