In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold that is modular, in the sense that the $L$-function of its middle-dimensional cohomology is associated with a classical modular form of weight 4 and level 55.

Keywords:

Calabi-Yau threefold, non-rigid Calabi-Yau threefold, two-dimensional Galois representation, modular variety, Horrocks-Mumford vector bundle Calabi-Yau threefold, non-rigid Calabi-Yau threefold, two-dimensional Galois representation, modular variety, Horrocks-Mumford vector bundle

MSC Classifications:

14J15, 11F23, 14J32, 11G40 show english descriptions Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
Relations with algebraic geometry and topology
Calabi-Yau manifolds
$L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 14J15 - Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
11F23 - Relations with algebraic geometry and topology
14J32 - Calabi-Yau manifolds
11G40 - $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]

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