Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
Algebraic Geometry
2022-08-03 v2 High Energy Physics - Theory
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 using Gromov-Witten theory. When 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.
Keywords
Cite
@article{arxiv.2201.11540,
title = {Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds},
author = {Yalong Cao and Georg Oberdieck and Yukinobu Toda},
journal= {arXiv preprint arXiv:2201.11540},
year = {2022}
}
Comments
25 pages. Published version. arXiv admin note: text overlap with arXiv:2201.10878