Disproof of modularity of moduli space of CY 3-folds of double covers of P3 ramified along eight planes in general positions

2007/09/07 by Ralf Gerkmann, Mao Sheng, Gerkmann, Ralf +3 · 1 citation
Computer Science · Mathematics · #14J10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0709.1051

openalex publication_date 2007/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the moduli space of Calabi-Yau 3-folds coming from eight planes of P³ in general positions is not modular. In fact we show the stronger statement that the Zariski closure of the monodromy group is actually the whole Sp(20,R). We construct an interesting submoduli, which we call hyperelliptic locus, over which the weight 3 Q-Hodge structure is the third wedge product of the weight 1 Q-Hodge structure on the corresponding hyperelliptic curve. The non-extendibility of the hyperelliptic locus inside the moduli space of a genuine Shimura subvariety is proved.

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• Examples of Calabi-Yau threefolds parametrised by Shimura varieties

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