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Mathematics > Algebraic Geometry

arXiv:2201.01645 (math)
[Submitted on 5 Jan 2022 (v1), last revised 14 Mar 2023 (this version, v2)]

Title:On quasi-tame Looijenga pairs

Authors: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.
Comments: 15 pages. v2: minor changes, explanations added, 18 pages. Version accepted for publication on Commun. Num. Theor. Phys
Subjects: Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Symplectic Geometry (math.SG)
Cite as: arXiv:2201.01645 [math.AG]
  (or arXiv:2201.01645v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2201.01645

Submission history

From: Andrea Brini [view email]
[v1] Wed, 5 Jan 2022 15:04:23 UTC (22 KB)
[v2] Tue, 14 Mar 2023 16:22:07 UTC (27 KB)
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