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arXiv · 1111.6422

Homogeneous components in the moduli space of sheaves and Virasoro characters

A. Buryak·B. L. Feigin
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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.

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BibTeXRIS

A. Buryak, B. L. Feigin. 2011-11-28. Homogeneous components in the moduli space of sheaves and Virasoro characters. https://doi.org/10.1016/j.geomphys.2012.02.011

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