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Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes (1206.5640v2)
Published 25 Jun 2012 in math.AG and math.CO
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 $\hat{sl}_m$.