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Hypergeometric local systems over $\mathbb{Q}$ with Hodge vector $(1,1,1,1)$

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arxiv 2401.13529 v1 pith:PVZSNNGI submitted 2024-01-24 math.AG math.NT

Giulia Gugiatti , Fernando Rodriguez Villegas This is my paper · ORCID
classification math.AGmath.NT
keywords hodgelocalsystemscaseshypergeometricmathbbpointvector
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abstract

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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Explicit Hypergeometric Modularity Method III

    math.NT 2026-07 conditional novelty 7.0 of 10

    An explicit algorithm matches length-4 hypergeometric sums to weight-4 modular forms and constructs nine forms for rigid Calabi-Yau threefolds.

  2. Preserving Hodge Vectors of Lattice Polytopes

    math.CO 2026-02 conditional novelty 7.0 of 10

    For lattice polytopes P1,...,Pk in a k-dimensional subspace and Q of dimension d, the Hodge vector of their Cayley polytope is MV(P1,...,Pk) times the Hodge vector of the projection of Q along that subspace.

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