@inbook{5250793dfb9b43cfa4c6349f2ab1050e,
title = "Quadratic Twists of Rigid Calabi–Yau Threefolds Over",
abstract = "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).",
author = "Gouv{\^e}a, {Fernando Q.} and Ian Kiming and Noriko Yui",
year = "2013",
doi = "10.1007/978-1-4614-6403-7_20",
language = "English",
isbn = "978-1-4614-6402-0",
volume = "3",
series = "Fields Institute Communications",
publisher = "Springer Science+Business Media",
pages = "517--533",
editor = "Radu Laza and Matthias Sch{\"u}tt and Noriko Yui",
booktitle = "Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds",
address = "Singapore",
}