Elliptic fibrations on K3 surfaces with a non-symplectic involution fixing rational curves and a curve of positive genus

Alice Garbagnati*, Cecilia Salgado

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)

Abstract

In this paper we complete the classification of the elliptic fibrations on :K3 surfaces which admit a non-symplectic involution acting trivially on the Neron-Severi group. We use the geometric method introduced by Oguiso and moreover we provide a geometric construction of the fibrations classified. If the non-symplectic involution fixes at least one curve of genus 1, we relate all the elliptic fibrations on the K3 surface with either elliptic fibrations or generalized conic bundles on rational elliptic surfaces. This description allows us to write the Weierstrass equations of the elliptic fibrations on the K3 surfaces explicitly and to study their specializations.

Original languageEnglish
Pages (from-to)1167-1206
Number of pages40
JournalRevista Matemática Iberoamericana
Volume36
Issue number4
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Elliptic fibrations
  • rational elliptic surfaces
  • K3 surfaces
  • double covers
  • WEIERSTRASS EQUATIONS
  • JACOBIAN FIBRATIONS

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