Hypergeometric local systems over $\mathbb{Q}$ with Hodge vector $(1,1,1,1)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929222145015808 |
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| author | Gugiatti, Giulia Villegas, Fernando Rodriguez |
| author_facet | Gugiatti, Giulia Villegas, Fernando Rodriguez |
| contents | We consider all irreducible rank-4 hypergeometric local systems defined over $\mathbb{Q}$ that support a rational one-dimensional variation of Hodge structures of weight 3 and Hodge vector $(1,1,1,1)$. Up to a natural equivalence there are only 47 cases. The first 14 cases have maximally unipotent monodromy at one point and have been extensively studied in the literature. We show that all 47 local systems are associated to families of generically smooth threefolds and we analyze the geometry and arithmetic at their conifold point. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_13529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypergeometric local systems over $\mathbb{Q}$ with Hodge vector $(1,1,1,1)$ Gugiatti, Giulia Villegas, Fernando Rodriguez Algebraic Geometry Number Theory 33Cxx, 14D07, 11F67 We consider all irreducible rank-4 hypergeometric local systems defined over $\mathbb{Q}$ that support a rational one-dimensional variation of Hodge structures of weight 3 and Hodge vector $(1,1,1,1)$. Up to a natural equivalence there are only 47 cases. The first 14 cases have maximally unipotent monodromy at one point and have been extensively studied in the literature. We show that all 47 local systems are associated to families of generically smooth threefolds and we analyze the geometry and arithmetic at their conifold point. |
| title | Hypergeometric local systems over $\mathbb{Q}$ with Hodge vector $(1,1,1,1)$ |
| topic | Algebraic Geometry Number Theory 33Cxx, 14D07, 11F67 |
| url | https://arxiv.org/abs/2401.13529 |