Refined curve counting with descendants and quantum mirrors

Fuente: arXiv
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Main Authors: Kennedy-Hunt, Patrick, Shafi, Qaasim, Kumaran, Ajith Urundolil
Format: Preprint
Published: 2025
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author Kennedy-Hunt, Patrick
Shafi, Qaasim
Kumaran, Ajith Urundolil
author_facet Kennedy-Hunt, Patrick
Shafi, Qaasim
Kumaran, Ajith Urundolil
contents Given a log Calabi--Yau surface $(Y,D)$, Bousseau has constructed a quantization of the mirror algebra of this pair. We give a formula for structure constants of this quantization in terms of higher genus descendant logarithmic Gromov--Witten invariants of $(Y,D)$. Our result generalises the weak Frobenius structure conjecture for surfaces to the $q$-refined setting, and is proved by relating these invariants to counts of quantum broken lines in the associated quantum scattering diagram.
format Preprint
id arxiv_https___arxiv_org_abs_2502_17236
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Refined curve counting with descendants and quantum mirrors
Kennedy-Hunt, Patrick
Shafi, Qaasim
Kumaran, Ajith Urundolil
Algebraic Geometry
Given a log Calabi--Yau surface $(Y,D)$, Bousseau has constructed a quantization of the mirror algebra of this pair. We give a formula for structure constants of this quantization in terms of higher genus descendant logarithmic Gromov--Witten invariants of $(Y,D)$. Our result generalises the weak Frobenius structure conjecture for surfaces to the $q$-refined setting, and is proved by relating these invariants to counts of quantum broken lines in the associated quantum scattering diagram.
title Refined curve counting with descendants and quantum mirrors
topic Algebraic Geometry
url https://arxiv.org/abs/2502.17236