Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds

Abstract

As an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold $X$ using Gromov-Witten theory. When $X$ is holomorphic symplectic, Gromov-Witten invariants vanish and one can consider the corresponding reduced theory. In a companion work, we propose a definition of Gopakumar-Vafa type invariants for such a reduced theory. In this paper, we give them a sheaf theoretic interpretation via moduli spaces of stable pairs.

arXiv comment25 pages. Published version. arXiv admin note: text overlap with arXiv:2201.10878

References in corpus (22)

• The intrinsic normal cone
• Curve counting via stable pairs in the derived category
• Stable pairs and BPS invariants
• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• Enumerative geometry of Calabi-Yau 4-folds
• Chern Classes of Tautological Sheaves on Hilbert Schemes
• Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds
• Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
• Orientability for gauge theories on Calabi-Yau manifolds
• Gromov-Witten invariants of the Hilbert schemes of points of a K3 surface
• Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• Stable pair invariants of local Calabi-Yau 4-folds
• Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Counting perverse coherent systems on Calabi-Yau 4-folds
• Degeneracy loci, virtual cycles and nested Hilbert schemes II
• Reduced Donaldson-Thomas invariants and the ring of dual numbers

Cited by in corpus (2)

• Open/Closed BPS Correspondence and Integrality
• Enumerative geometry of surfaces and topological strings