arXiv 2201.016452022-01math.AGhep-thmath-phmath.MPmath.SG

On quasi-tame Looijenga pairs

Andrea Brini, Yannik Schuler

备注：: 15 pages. v2: minor changes, explanations added, 18 pages. Version accepted for publication on Commun. Num. Theor. Phys

英文摘要：

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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