Comparison of non-archimedean and logarithmic mirror constructions via the Frobenius structure theorem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915085657571328 |
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| author | Johnston, Sam |
| author_facet | Johnston, Sam |
| contents | For a log Calabi Yau pair (X,D) with X\D smooth affine, satisfying either assumption 1.1 of "The canonical wall structure and intrinsic mirror symmetry" or contains a Zariski dense torus, we prove under the condition that D is the support of a nef divisor, that the structure constants defining a trace form on the mirror algebra constructed by Gross-Siebert are given by the naive curve counts defined by Keel-Yu in definition 1.1 of "The Frobenius structure theorem for log Calabi-Yau varieties containing a torus". As a corollary, we deduce the equality of the mirror algebras constructed by Gross-Siebert and Keel-Yu in the case X\D contains a Zariski dense torus. In addition, we use this result to prove a mirror conjecture proposed by Mandel in "Fano mirror periods from the Frobenius structure conjecture" for Fano pairs satisfying assumption 1.1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_00940 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Comparison of non-archimedean and logarithmic mirror constructions via the Frobenius structure theorem Johnston, Sam Algebraic Geometry For a log Calabi Yau pair (X,D) with X\D smooth affine, satisfying either assumption 1.1 of "The canonical wall structure and intrinsic mirror symmetry" or contains a Zariski dense torus, we prove under the condition that D is the support of a nef divisor, that the structure constants defining a trace form on the mirror algebra constructed by Gross-Siebert are given by the naive curve counts defined by Keel-Yu in definition 1.1 of "The Frobenius structure theorem for log Calabi-Yau varieties containing a torus". As a corollary, we deduce the equality of the mirror algebras constructed by Gross-Siebert and Keel-Yu in the case X\D contains a Zariski dense torus. In addition, we use this result to prove a mirror conjecture proposed by Mandel in "Fano mirror periods from the Frobenius structure conjecture" for Fano pairs satisfying assumption 1.1. |
| title | Comparison of non-archimedean and logarithmic mirror constructions via the Frobenius structure theorem |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2204.00940 |