Modularity of a nonrigid Calabi–Yau manifold with bad reduction at 13

Volume 90 / 2007

Grzegorz Kapustka, Michał Kapustka 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 $p\geq 5$.

Authors

  • Grzegorz KapustkaInstitute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland
    e-mail
  • Michał KapustkaJagiellonian University
    ul. Reymonta 4
    30-059 Kraków, Poland
    e-mail

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