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Quadratic Twists of Rigid Calabi–Yau Threefolds Over

Publikation: Bidrag til bog/antologi/rapportBidrag til bog/antologiForskningfagfællebedømt

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).
OriginalsprogEngelsk
TitelArithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds
RedaktørerRadu Laza, Matthias Schütt, Noriko Yui
Vol/bind3
Udgivelses stedNew York
ForlagSpringer Science+Business Media
Publikationsdato2013
Sider517-533
ISBN (Trykt)978-1-4614-6402-0
ISBN (Elektronisk)978-1-4614-6403-7
DOI
StatusUdgivet - 2013
NavnFields Institute Communications
Vol/bind67
ISSN1069-5265

ID: 48868277