Quadratic Twists of Rigid Calabi–Yau Threefolds Over
Publikation: Bidrag til bog/antologi/rapport › Bidrag til bog/antologi › Forskning › fagfællebedømt
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).
Originalsprog | Engelsk |
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Titel | Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds |
Redaktører | Radu Laza, Matthias Schütt, Noriko Yui |
Vol/bind | 3 |
Udgivelsessted | New York |
Forlag | Springer Science+Business Media |
Publikationsdato | 2013 |
Sider | 517-533 |
ISBN (Trykt) | 978-1-4614-6402-0 |
ISBN (Elektronisk) | 978-1-4614-6403-7 |
DOI | |
Status | Udgivet - 2013 |
Navn | Fields Institute Communications |
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Vol/bind | 67 |
ISSN | 1069-5265 |
ID: 48868277