Quadratic Twists of Rigid Calabi–Yau Threefolds Over
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Quadratic Twists of Rigid Calabi–Yau Threefolds Over. / Gouvêa, Fernando Q. ; Kiming, Ian; Yui, Noriko.
Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds. red. / Radu Laza; Matthias Schütt; Noriko Yui. Bind 3 New York : Springer Science+Business Media, 2013. s. 517-533 (Fields Institute Communications, Bind 67).Publikation: Bidrag til bog/antologi/rapport › Bidrag til bog/antologi › Forskning › fagfællebedømt
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TY - CHAP
T1 - Quadratic Twists of Rigid Calabi–Yau Threefolds Over
AU - Gouvêa, Fernando Q.
AU - Kiming, Ian
AU - Yui, Noriko
PY - 2013
Y1 - 2013
N2 - 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).
AB - 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).
U2 - 10.1007/978-1-4614-6403-7_20
DO - 10.1007/978-1-4614-6403-7_20
M3 - Book chapter
SN - 978-1-4614-6402-0
VL - 3
T3 - Fields Institute Communications
SP - 517
EP - 533
BT - Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds
A2 - Laza, Radu
A2 - Schütt, Matthias
A2 - Yui, Noriko
PB - Springer Science+Business Media
CY - New York
ER -
ID: 48868277