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.
Linear systems on rational elliptic surfaces and elliptic fibrations on K3 surfaces / A. Garbagnati, C. Salgado. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 223:1(2019 Jan), pp. 277-300. [10.1016/j.jpaa.2018.03.010]
Linear systems on rational elliptic surfaces and elliptic fibrations on K3 surfaces
A. Garbagnati
;
2019
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.File | Dimensione | Formato | |
---|---|---|---|
double_cover_rational_rev2.pdf
accesso riservato
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
415.76 kB
Formato
Adobe PDF
|
415.76 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
1-s2.0-S0022404918300690-main.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
559.54 kB
Formato
Adobe PDF
|
559.54 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.