Generating Series of the Poincaré Polynomials of Quasihomogeneous Hilbert Schemes

  title={Generating Series of the Poincar{\'e} Polynomials of Quasihomogeneous Hilbert Schemes},
  author={Alexandr Buryak and Boris Feigin},
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 \(\widehat{\mathit{sl}}_{m}\). 

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