Non-archimedean SYZ fibrations via tropical contractions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913304957419520 |
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| author | Yamamoto, Yuto |
| author_facet | Yamamoto, Yuto |
| contents | We consider a toric degeneration of Calabi--Yau complete intersections of Batyrev--Borisov in the Gross--Siebert program. The author showed in his previous work that there exists an integral affine contraction map called a tropical contraction, from the tropical variety obtained as its tropicalization to the dual intersection complex of the toric degeneration. In this article, we prove that the dual intersection complex is isomorphic to the essential skeleton of the Berkovich analytification as piecewise integral affine manifolds, and the composition of the tropicalization map and the tropical contraction is an affinoid torus fibration with a discriminant of codimension $2$, which induces the same integral affine structure as the one coming from the toric degeneration. This is a generalization of the earlier work by Pille-Schneider for a specific degeneration of Calabi--Yau hypersurfaces in projective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-archimedean SYZ fibrations via tropical contractions Yamamoto, Yuto Algebraic Geometry We consider a toric degeneration of Calabi--Yau complete intersections of Batyrev--Borisov in the Gross--Siebert program. The author showed in his previous work that there exists an integral affine contraction map called a tropical contraction, from the tropical variety obtained as its tropicalization to the dual intersection complex of the toric degeneration. In this article, we prove that the dual intersection complex is isomorphic to the essential skeleton of the Berkovich analytification as piecewise integral affine manifolds, and the composition of the tropicalization map and the tropical contraction is an affinoid torus fibration with a discriminant of codimension $2$, which induces the same integral affine structure as the one coming from the toric degeneration. This is a generalization of the earlier work by Pille-Schneider for a specific degeneration of Calabi--Yau hypersurfaces in projective spaces. |
| title | Non-archimedean SYZ fibrations via tropical contractions |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2404.04972 |