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Unramified Gromov-Witten and Gopakumar-Vafa invariants

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arxiv 2405.18398 v2 pith:SGZTHOGR submitted 2024-05-28 math.AG math-phmath.MPmath.SG

Denis Nesterov This is my paper · ORCID
classification math.AGmath-phmath.MPmath.SG
keywords invariantsgopakumar-vafaclassesgromov-wittenunramifiedalgebro-geometriccalabi-yaucase
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Kim, Kresch and Oh defined unramified Gromov-Witten invariants. For a threefold, Pandharipande conjectured that they are equal to Gopakumar-Vafa invariants (BPS invariants) in the case of Fano classes and primitive Calabi-Yau classes. We prove the conjecture using a wall-crossing technique. This provides an algebro-geometric construction of Gopakumar-Vafa invariants in these cases.

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Cited by 2 Pith papers

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

  1. Torelli loci, product cycles, and the homomorphism conjecture for $\mathcal{A}_g$

    math.AG 2026-01 conditional novelty 7.0 of 10

    For 2≤g≤8, taut([J_g]·[A_2×A_{g-2}]) = taut([J_g])·taut([A_2×A_{g-2}]), and similarly for ([J_6],[A_3×A_3]); the paper also constructs new Gorenstein-kernel classes in compact-type moduli spaces.

  2. BPS polynomials and Welschinger invariants

    math.AG 2025-06 conditional novelty 7.0 of 10

    The new BPS polynomials of surfaces specialize at q=-1 to Welschinger invariants for blowups of the projective plane at up to six points.

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