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.

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

References in corpus (1)

• Enumerative geometry of Calabi-Yau 4-folds

Cited by in corpus (2)

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