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Article

Homogeneous components in the moduli space of sheaves and Virasoro characters

Journal of Geometry and Physics. 2012. Vol. 62. No. 7. P. 1652-1664.
Feigin B. L., Буряк А. Ю.

The moduli space 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.