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arXiv · 2303.00503

All-genus WDVV recursion, quivers, and BPS invariants

Pierrick Bousseau·Longting Wu
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Abstract

Let $X$ be a smooth projective surface and $D$ a smooth rational ample divisor in $X$. We prove an all-genus generalization of the genus $0$ WDVV equation for primary Gromov--Witten invariants of the local 3-fold $\mathcal{O}_X(-D)$. The proof relies on a correspondence between all-genus Gromov--Witten invariants and refined Donaldson--Thomas invariants of acyclic quivers. In particular, the corresponding BPS invariants are expressed in terms of Betti numbers of moduli spaces of quiver representations.

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Pierrick Bousseau, Longting Wu. 2023-03-01. All-genus WDVV recursion, quivers, and BPS invariants. https://arxiv.org/abs/2303.00503

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