English

A note on BPS structures and Gopakumar-Vafa invariants

Algebraic Geometry 2019-05-23 v2 High Energy Physics - Theory

Abstract

We regard the work of Maulik and Toda, proposing a sheaf-theoretic approach to Gopakumar-Vafa invariants, as defining a BPS structure, that is, a collection of BPS invariants together with a central charge. Assuming their conjectures, we show that a canonical flat section of the flat connection corresponding to this BPS structure, at the level of formal power series, reproduces the Gromov-Witten partition function for all genera, up to some error terms in genus 0 and 1. This generalises a result of Bridgeland and Iwaki for the contribution from genus 0 Gopakumar-Vafa invariants.

Cite

@article{arxiv.1812.07454,
  title  = {A note on BPS structures and Gopakumar-Vafa invariants},
  author = {Jacopo Stoppa},
  journal= {arXiv preprint arXiv:1812.07454},
  year   = {2019}
}

Comments

v1: 15 pages. v2: 17 pages, exposition improved

R2 v1 2026-06-23T06:46:30.538Z