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

Alice Garbagnati ^[1] ; Cecília Salgado ^[2]
1. [1] University of Milan
  
  University of Milan
  
  Milán, Italia
2. [2] Universidade Federal do Rio de Janeiro
  
  Universidade Federal do Rio de Janeiro
  
  Brasil
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 4, 2020, págs. 1167-1206
Idioma: inglés
DOI: 10.4171/rmi/1163
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Resumen
- In this paper we complete the classification of the elliptic fibrations on K3 surfaces which admit a non-symplectic involution acting trivially on the Néron–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.