Work

Refined curve counting with descendants and quantum mirrors

Year: 2026

Type: article

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

Source: Épijournal de Géométrie Algébrique

DOI: 10.46298/epiga.2026.15425

Authors: Patrick Kennedy-Hunt, Qaasim Shafi, Ajith Urundolil Kumaran

Institution: University of Cambridge

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: UK Research and Innovation, London Mathematical Society, HORIZON EUROPE European Research Council

Awards: G6983759150, Correspondences in enumerative geometry: Hilbert schemes, K3 surfaces and modular forms