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arXiv · 2201.01645

On quasi-tame Looijenga pairs

Andrea Brini·Yannik Schuler
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Abstract

We prove a conjecture of Bousseau, van Garrel and the first-named author relating, under suitable positivity conditions, the higher genus maximal contact log Gromov-Witten invariants of Looijenga pairs to other curve counting invariants of Gromov-Witten/Gopakumar-Vafa type. The proof consists of a closed-form $q$-hypergeometric resummation of the quantum tropical vertex calculation of the log invariants in presence of infinite scattering. The resulting identity of $q$-series appears to be new and of independent combinatorial interest.

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Andrea Brini, Yannik Schuler. 2023-03-14. On quasi-tame Looijenga pairs. https://arxiv.org/abs/2201.01645

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