The modularity of the Barth-Nieto quintic and its relatives

Klaus Hulek, J. Spandaw, B. Van Geemen & D. Van Straten
The moduli space of (1, 3)-polarized abelian surfaces with full level-2 structure is birational to a double cover of the Barth Nieto quintic. Barth and Nieto have shown that these varieties have Calabi-Yau models Z and Y, respectively. In this paper we apply the Weil conjectures to show that Y and Z are rigid and we prove that the L-function of their common third e A tale cohomology group is modular, as predicted by a...
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