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Patrick Kennedy-Hunt ; Qaasim Shafi ; Ajith Urundolil Kumaran - Refined curve counting with descendants and quantum mirrors
epiga:15425 - Épijournal de Géométrie Algébrique, April 14, 2026, Volume 10 - https://doi.org/10.46298/epiga.2026.15425Refined curve counting with descendants and quantum mirrorsArticle
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: arXiv.org:2502.17236
Volume: Volume 10
Published on: April 14, 2026
Accepted on: October 8, 2025
Submitted on: March 26, 2025
Keywords: Algebraic Geometry
Classifications
Mathematics Subject Classification 20201
- 14A21 - Logarithmic algebraic geometry, log schemes
- 14J33 - Mirror symmetry (algebro-geometric aspects)
- 14N10 - Enumerative problems (combinatorial problems) in algebraic geometry
- 14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
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