Homogeneous components in the moduli space of sheaves and Virasoro characters

Details Homogeneous components in the moduli space of sheaves and Virasoro characters Homogeneous components in the moduli space of sheaves and Virasoro characters

2011-11-28

arxiv.org/abs/1111.6422v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

The moduli space 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.

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