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

2020/07/28 by Cantoral-Farfán, Victoria, Garbagnati, Alice, Salgado, Cecília +2
#Algebraic Geometry (math.AG) #Double covers #Elliptic fibrations #Extremal rational elliptic surfaces #FOS: Mathematics #K3 surfaces

paper · doi:10.48550/arxiv.2007.14043

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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