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

Victoria Cantoral Fardan, Alice Garbagnati, Cecília Salgado Guimarães da Silva, Antonela Trbovic, Rosa Winter

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

2 Citations (Scopus)

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 the 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.
Original languageEnglish
Title of host publicationWomen in Numbers Europe III
Subtitle of host publicationResearch Directions in Number Theory
EditorsAlina Carmen Cojocaru, Sorina Ionica, Elisa Lorenzo García
PublisherSpringer
Pages171-205
ISBN (Electronic)978-3-030-77700-5
ISBN (Print)978-3-030-77699-2
DOIs
Publication statusPublished - 2021
Externally publishedYes

Publication series

NameAssociation for Women in Mathematics Series
PublisherSpringer
Volume24

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