Geodesic
Modularity of a nonrigid Calabi–Yau manifold with bad reduction at 13
Grzegorz Kapustka1 ; Michał Kapustka2
1 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
2 Jagiellonian University ul. Reymonta 4 30-059 Kraków, Poland
Annales Polonici Mathematici, Tome 90 (2007) no. 1, pp. 89-98.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $p\geq 5$.
DOI : 10.4064/ap90-1-7
Keywords: identify weight newform modular calabi yau manifold studied hulek verrill main obstacle calabi yau manifold rigid has bad reduction prime replacing original fiber product elliptic fibrations fiberwise kummer construction reduce problem studying modularity rigid calabi yau manifold reduction primes geq

Grzegorz Kapustka 1 ; Michał Kapustka 2

1 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
2 Jagiellonian University ul. Reymonta 4 30-059 Kraków, Poland 
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Grzegorz Kapustka; Michał Kapustka. Modularity of a nonrigid Calabi–Yau manifold
 with bad reduction at 13. Annales Polonici Mathematici, Tome 90 (2007) no. 1, pp. 89-98. doi : 10.4064/ap90-1-7. http://geodesic.mathdoc.fr/articles/10.4064/ap90-1-7/

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