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

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arxiv 1009.1775 v3 pith:UZCSC2NU submitted 2010-09-09 math-ph hep-thmath.AGmath.MP

Jan Manschot This is my paper · ORCID
classification math-phhep-thmath.AGmath.MP
keywords bettiblow-upfunctionsnumbersgeneratingmoduliranksheaves
verification ladder T0 review T1 audit T2 compute T3 formal
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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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  1. Mock modularity of Calabi-Yau threefolds

    hep-th 2024-11 conditional novelty 6.0 of 10

    The paper constructs explicit indefinite theta series solving the modular anomaly for rank 0 DT invariants, fixing these generating functions up to modular forms determined by polar terms.

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