A Modular Non-Rigid Calabi-Yau Threefold

Details A Modular Non-Rigid Calabi-Yau Threefold A Modular Non-Rigid Calabi-Yau Threefold

2005-08-07

arxiv.org/abs/math/0508127v2

Mathematics

Algebraic Geometry

34 pages; To appear in "Mirror Symmetry V", Proceedings of the BIRS Workshop on Calabi-Yau Varieties and Mirror Symmetry, Dece

Scientific paper

We construct an algebraic variety by resolving singularities of a quintic Calabi-Yau threefold. The middle cohomology of the threefold is shown to contain a piece coming from a pair of elliptic surfaces. The resulting quotient is a two-dimensional Galois representation. By using the Lefschetz fixed-point theorem in \'etale cohomology and counting points on the variety over finite fields, this Galois representation is shown to be modular.

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