Modularity of a nonrigid Calabi–Yau manifold with bad reduction at 13
Volume 90 / 2007
Annales Polonici Mathematici 90 (2007), 89-98
MSC: 14G10, 14J32.
DOI: 10.4064/ap90-1-7
Abstract
We identify the weight four newform of a modular Calabi–Yau manifold studied by Hulek and Verrill. The main obstacle is that this Calabi–Yau manifold is not rigid and has bad reduction at prime 13. Replacing the original fiber product of elliptic fibrations with a fiberwise Kummer construction we reduce the problem to studying the modularity of a rigid Calabi–Yau manifold with good reduction at primes $p\geq 5$.
