Log Calabi-Yau mirror symmetry and non-archimedean disks
| Autor: | Keel, Sean, YU, Tony Yue |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We construct the mirror algebra to a smooth affine log Calabi-Yau variety with maximal boundary, as the spectrum of a commutative associative algebra with a canonical basis, whose structure constants are given as naive counts of non-archimedean analytic disks. More generally, we studied the enumeration of non-archimedean analytic curves with boundaries, associated to a given transverse spine in the essential skeleton of the log Calabi-Yau variety. The moduli spaces of such curves are infinite dimensional. In order to obtain finite counts, we impose a boundary regularity condition so that the curves can be analytically continued into tori, that are unrelated to the given log Calabi-Yau variety. We prove the properness of the resulting moduli spaces, and show that the mirror algebra is a finitely generated commutative associative algebra, giving rise to a mirror family of log Calabi-Yau varieties. Comment: 60 pages, comments welcome |
| Databáze: | arXiv |
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