Linear systems on rational elliptic surfaces and elliptic fibrations on K3 surfaces

Alice Garbagnati*, Cecília Salgado

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)

Abstract

We consider K3 surfaces which are double covers of rational elliptic surfaces. The former are endowed with a natural elliptic fibration, which is induced by the latter. There are also other elliptic fibrations on such K3 surfaces, which are necessarily induced by special linear systems on the rational elliptic surfaces. We describe these linear systems. In particular, we observe that every conic bundle on the rational surface induces a genus 1 fibration on the K3 surface and we classify the singular fibers of the genus 1 fibration on the K3 surface it terms of singular fibers and special curves on the conic bundle on the rational surface.
Original languageEnglish
Pages (from-to)277-300
Number of pages24
JournalJournal of pure and applied algebra
Volume223
Issue number1
DOIs
Publication statusPublished - Jan-2019
Externally publishedYes

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