Refined curve counting with descendants and quantum mirrors
Abstract
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. Journal version
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Mathematical Identities
Data Management and Algorithms
Publication details
- Journal / source
- Épijournal de Géométrie Algébrique
- Volume
- Volume 10
- Publication date
- 14 April 2026
- Language
- EN