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arXiv · 2007.14043

Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces

Victoria Cantoral-Farfán·Alice Garbagnati·Cecília Salgado·Antonela Trbović·Rosa Winter
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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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Victoria Cantoral-Farfán, Alice Garbagnati, Cecília Salgado, Antonela Trbović, Rosa Winter. 2020-07-28. Fields of definition of elliptic fibrations on covers of certain extremal rational elliptic surfaces. https://arxiv.org/abs/2007.14043

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