On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces

Helena Verrill; Klaus Hulek

On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces

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arxiv math/0502158 v1 pith:6CRAEHY3 submitted 2005-02-08 math.AG math.NT

Klaus Hulek , Helena Verrill This is my paper · ORCID

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keywords calabi-yauthreefoldsellipticmodularityrigidruledcontaincontaining

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We prove that (not necessarily rigid) Calabi-Yau threefolds defined over the rationals which contain sufficiently many elliptic ruled surfcaes are modular (under mild restrictions on the primes of bad reduction). Our proof uses the results of Dieulefait and Manoharmayum who proved modularity of rigid Calabi-Yau threefolds.

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Fano and Reflexive Polytopes from Feynman Integrals
hep-th 2025-12 unverdicted novelty 6.0 of 10

Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.

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