Elliptic Fibrations of a certain K3 surface of the Apéry–Fermi pencil
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2022), pp. 5-36.

We explain how to obtain from Kneser–Nishiyama’s method all the elliptic fibrations of the singular (i.e. of Picard number 20) K3 surface Y 10 of discriminant 72 and belonging to the Apéry–Fermi pencil (Y k ). The case of its extremal elliptic fibrations is developped together with Weierstrass equations, noticing that two of them are obtained by 3-isogeny from extremal fibrations of the K3 surface Y 2 of discriminant 8.

On montre comment la méthode de Kneser–Nishiyama permet d’obtenir toutes les fibrations elliptiques de la surface K3 singulière (i.e. de nombre de Picard 20) de discriminant 72, notée Y 10 , appartenant au pinceau (Y k ) de surfaces K3 d’Apéry–Fermi. Les fibrations elliptiques extrémales sont en outre données avec des équations de Weierstrass. On remarque que deux d’entre elles sont obtenues par 3-isogénie à partir de fibrations extrémales de la surface Y 2 de discriminant 8.

Received:
Published online:
DOI: 10.5802/pmb.44
Classification: 11F23, 11G05, 14J28, 14J27
Keywords: Niemeier Lattices, Kneser–Nishiyama Method for Elliptic Fibrations of $K3$ Surfaces, Elkies r-neighbor Method for Weierstrass Equations
Marie José Bertin 1; Odile Lecacheux 1

1 Sorbonne Université, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Case 247, 4 Place Jussieu, 75252 PARIS, Cedex 85, France
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Marie José Bertin; Odile Lecacheux. Elliptic Fibrations of a certain $K3$ surface of the Apéry–Fermi pencil. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2022), pp. 5-36. doi : 10.5802/pmb.44. https://pmb.centre-mersenne.org/articles/10.5802/pmb.44/

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