We study K3 surfaces over a number field k which are double covers of extremal rational elliptic surfaces. We provide a list of all elliptic fibrations on certain K3 surfaces together with the degree of a field extension over which each genus one fibration is defined and admits a section. We show that the latter depends, in general, on the action of the cover involution on the fibers of the genus 1 fibration.
Fields of Definition of Elliptic Fibrations on Covers of Certain Extremal Rational Elliptic Surfaces / V. Cantoral-Farfan, A. Garbagnati, C. Salgado, A. Trbovic, R. Winter (ASSOCIATION FOR WOMEN IN MATHEMATICS SERIES). - In: Women in Numbers Europe III : Research Directions in Number Theory / [a cura di] A.C. Cojocaru, S. Ionica, E.L. García. - [s.l] : Springer Science and Business Media, 2021. - ISBN 978-3-030-77699-2. - pp. 171-205 [10.1007/978-3-030-77700-5_6]
Fields of Definition of Elliptic Fibrations on Covers of Certain Extremal Rational Elliptic Surfaces
A. GarbagnatiSecondo
;
2021
Abstract
We study K3 surfaces over a number field k which are double covers of extremal rational elliptic surfaces. We provide a list of all elliptic fibrations on certain K3 surfaces together with the degree of a field extension over which each genus one fibration is defined and admits a section. We show that the latter depends, in general, on the action of the cover involution on the fibers of the genus 1 fibration.
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