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April, 2020 Apéry–Fermi pencil of $K3$-surfaces and 2-isogenies
Marie José BERTIN, Odile LECACHEUX
J. Math. Soc. Japan 72(2): 599-637 (April, 2020). DOI: 10.2969/jmsj/80638063

Abstract

Given a generic $K3$-surface $Y_k$ of the Apéry–Fermi pencil, we use the Kneser–Nishiyama technique to determine all its non isomorphic elliptic fibrations. These computations lead to determine those fibrations with 2-torsion sections T. We classify the fibrations such that the translation by T gives a Shioda–Inose structure. The other fibrations correspond to a $K3$-surface identified by its transcendental lattice. The same problem is solved for a singular member $Y_2$ of the family showing the differences with the generic case. In conclusion we put our results in the context of relations between 2-isogenies and isometries on the singular surfaces of the family.

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Marie José BERTIN. Odile LECACHEUX. "Apéry–Fermi pencil of $K3$-surfaces and 2-isogenies." J. Math. Soc. Japan 72 (2) 599 - 637, April, 2020. https://doi.org/10.2969/jmsj/80638063

Information

Received: 26 May 2018; Revised: 17 October 2018; Published: April, 2020
First available in Project Euclid: 16 October 2019

zbMATH: 07196914
MathSciNet: MR4090348
Digital Object Identifier: 10.2969/jmsj/80638063

Subjects:
Primary: 14J28
Secondary: 11G05 , 14H52 , 14J27 , 14J50

Keywords: elliptic fibrations of $K3$-surfaces , isogenies , Morrison–Nikulin involutions

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 2 • April, 2020
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