Refined curve counting with descendants and quantum mirrors
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866913162926751744 |
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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 |