# 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.