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arXiv · 1812.07454

A note on BPS structures and Gopakumar-Vafa invariants

Jacopo Stoppa
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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.

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Jacopo Stoppa. 2019-05-22. A note on BPS structures and Gopakumar-Vafa invariants. https://arxiv.org/abs/1812.07454

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