Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions

Abstract

The Gopakumar-Vafa type invariants on Calabi-Yau 4-folds (which are non-trivial only for genus zero and one) are defined by Klemm-Pandharipande from Gromov-Witten theory, and their integrality is conjectured. In a previous work of Cao-Maulik-Toda, ${\mathrm{DT}}_4$ invariants with primary insertions on moduli spaces of one dimensional stable sheaves are used to give a sheaf theoretical interpretation of the genus zero GV type invariants. In this paper, we propose a sheaf theoretical interpretation of the genus one GV type invariants using descendent insertions on the above moduli spaces. The conjectural formula in particular implies nontrivial constraints on genus zero GV type (equivalently GW) invariants of CY 4-folds which can be proved by the WDVV equation.

arXiv comment21 pages. Published version

References in corpus (10)

• Curve counting via stable pairs in the derived category
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• Relative Lefschetz Action and BPS State Counting
• Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds
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• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
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• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
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Cited by in corpus (11)

• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• Canonical vertex formalism in DT theory of toric Calabi-Yau 4-folds
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Counting perverse coherent systems on Calabi-Yau 4-folds
• The Origin of Calabi-Yau Crystals in BPS States Counting
• WDVV equations and invariant bi-Hamiltonian formalism
• Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
• Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
• An Overview of Crystals and Double Quiver Yangians