Elliptic fibrations on K3 surfaces with a non-symplectic involution fixing rational curves and a curve of positive genus
Articolo
Data di Pubblicazione:
2020
Citazione:
Elliptic fibrations on K3 surfaces with a non-symplectic involution fixing rational curves and a curve of positive genus / A. Garbagnati, C. Salgado. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 36:4(2020), pp. 1167-1206. [10.4171/RMI/1163]
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 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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Double covers; Elliptic fibrations; K3 surfaces; Rational elliptic surfaces
Elenco autori:
A. Garbagnati, C. Salgado
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