On quasi-tame Looijenga pairs
Algebraic Geometry
2023-03-15 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Symplectic Geometry
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 -hypergeometric resummation of the quantum tropical vertex calculation of the log invariants in presence of infinite scattering. The resulting identity of -series appears to be new and of independent combinatorial interest.
Cite
@article{arxiv.2201.01645,
title = {On quasi-tame Looijenga pairs},
author = {Andrea Brini and Yannik Schuler},
journal= {arXiv preprint arXiv:2201.01645},
year = {2023}
}
Comments
15 pages. v2: minor changes, explanations added, 18 pages. Version accepted for publication on Commun. Num. Theor. Phys