Gopakumar-Vafa invariants and wall-crossing
Algebraic Geometry
2022-02-08 v4 High Energy Physics - Theory
Abstract
In this paper, we generalize a mathematical definition of Gopakumar-Vafa (GV) invariants on Calabi-Yau 3-folds introduced by Maulik and the author, using an analogue of BPS sheaves introduced by Davison-Meinhardt on the coarse moduli spaces of one dimensional twisted semistable sheaves with arbitrary holomorphic Euler characteristics. We show that our generalized GV invariants are independent of twisted stability conditions, and conjecture that they are also independent of holomorphic Euler characteristics, so that they define the same GV invariants. As an application, we will show the flop transformation formula of GV invariants.
Cite
@article{arxiv.1710.01843,
title = {Gopakumar-Vafa invariants and wall-crossing},
author = {Yukinobu Toda},
journal= {arXiv preprint arXiv:1710.01843},
year = {2022}
}
Comments
53 pages, Appendix A is removed and the proof of Prop 5.3 is modified