Quadratic Twists of Rigid Calabi–Yau Threefolds Over
Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
We consider rigid Calabi–Yau threefolds defined over Q and the question of whether they admit quadratic twists. We give a precise geometric definition of the notion of a quadratic twists in this setting. Every rigid Calabi–Yau threefold over Q is modular so there is attached to it a certain newform of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N) and integral Fourier coefficients arise from rigid Calabi–Yau threefolds defined over Q (a geometric realization problem).
Original language | English |
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Title of host publication | Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds |
Editors | Radu Laza, Matthias Schütt, Noriko Yui |
Volume | 3 |
Place of Publication | New York |
Publisher | Springer Science+Business Media |
Publication date | 2013 |
Pages | 517-533 |
ISBN (Print) | 978-1-4614-6402-0 |
ISBN (Electronic) | 978-1-4614-6403-7 |
DOIs | |
Publication status | Published - 2013 |
Series | Fields Institute Communications |
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Volume | 67 |
ISSN | 1069-5265 |
ID: 48868277