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Refined curve counting with descendants and quantum mirrors

2025/02/24 by Patrick Kennedy–Hunt, Patrick Kennedy-Hunt, Kennedy-Hunt, Patrick +4
Mathematics · Computer Science · #math.AG

paper · pdf · doi:10.46298/epiga.2026.15425

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.

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