The Betti numbers of the moduli space of stable sheaves of rank 3 on P2

Details The Betti numbers of the moduli space of stable sheaves of rank 3 on P2 The Betti numbers of the moduli space of stable sheaves of rank 3 on P2

2010-09-09

arxiv.org/abs/1009.1775v3

Lett.Math.Phys.98:65-78,2011

Physics

Mathematical Physics

15 pages, final version

Scientific paper

10.1007/s11005-011-0490-0

This article computes the generating functions of the Betti numbers of the moduli space of stable sheaves of rank 3 on the projective plane P2 and its blow-up. Wall-crossing is used to obtain the Betti numbers on the blow-up. These can be derived equivalently using flow trees, which appear in the physics of BPS-states. The Betti numbers for P2 follow from those for the blow-up by the blow-up formula. The generating functions are expressed in terms of modular functions and indefinite theta functions.

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