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

Ralf Gerkmann, Sheng Mao, Kang Zuo

Number 38
Authors Mao Sheng
Ralf Gerkmann
Kang Zuo
Year 2007

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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