关于拟驯服的Looijenga对

IF 1.2 3区数学 Q1 MATHEMATICS

Communications in Number Theory and Physics Pub Date : 2022-01-05 DOI:10.4310/cntp.2023.v17.n2.a3

A. Brini, Yannik Schuler

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引用次数: 2

摘要

在适当的正性条件下，证明了Bousseau、van Garrel等人关于Looijenga对的高格极大接触对数Gromov-Witten不变量与其他Gromov-Witten/Gopakumar-Vafa型曲线计数不变量的一个猜想。该证明由无限散射存在下对数不变量的量子热带顶点计算的一个闭合形式$q$-超几何恢复组成。由此得到的$q$系列的恒等式似乎是新的，具有独立的组合意义。

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On quasi-tame Looijenga pairs

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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来源期刊

Communications in Number Theory and Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Focused on the applications of number theory in the broadest sense to theoretical physics. Offers a forum for communication among researchers in number theory and theoretical physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields.