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 language | English |
---|---|
Pages (from-to) | 1167-1206 |
Number of pages | 40 |
Journal | Revista Matemática Iberoamericana |
Volume | 36 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2020 |
Externally published | Yes |
Keywords
- Elliptic fibrations
- rational elliptic surfaces
- K3 surfaces
- double covers
- WEIERSTRASS EQUATIONS
- JACOBIAN FIBRATIONS