On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces
Algebraic Geometry
2007-05-23 v1 Number Theory
Abstract
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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Cite
@article{arxiv.math/0502158,
title = {On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces},
author = {Klaus Hulek and Helena Verrill},
journal= {arXiv preprint arXiv:math/0502158},
year = {2007}
}
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17 pages