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BPS invariants of semi-stable sheaves on rational surfaces

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arxiv 1109.4861 v3 pith:JPAMG4Z3 submitted 2011-09-22 math-ph hep-thmath.AGmath.MP

Jan Manschot This is my paper · ORCID
classification math-phhep-thmath.AGmath.MP
keywords invariantsrationalsheavessurfacesappliedformulahirzebruchother
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BPS invariants are computed, capturing topological invariants of moduli spaces of semi-stable sheaves on rational surfaces. For a suitable stability condition, it is proposed that the generating function of BPS invariants of a Hirzebruch surface takes the form of a product formula. BPS invariants for other stability conditions and other rational surfaces are obtained using Harder-Narasimhan filtrations and the blow-up formula. Explicit expressions are given for rank <4 sheaves on a Hirzebruch surface or the projective plane. The applied techniques can be applied iteratively to compute invariants for higher rank.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Refined Vafa-Witten invariants for toric surfaces from supersymmetric localization in 5D gauge theory

    hep-th 2026-07 conditional novelty 6.0 of 10

    5D N=1* supersymmetric localization on toric surfaces equals refined Vafa–Witten invariants for odd first Chern class; the even-c1 case fails without a hand-added constant.

  2. BPS Dendroscopy on Local $\mathbb{P}^1\times \mathbb{P}^1$

    hep-th 2024-12 unverdicted novelty 6.0 of 10

    Construction of the scattering diagram for BPS indices on local P1 x P1 and sketch of the Split Attractor Flow Tree Conjecture for restricted central charge phase.

  3. 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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