In this paper we classify the elliptic fibrations on K3 surfaces which are the double cover of a blow up of P^2 branched along rational curves and we give equations for many of these elliptic fibrations. Thus we obtain a classification of the van Geemen–Sarti involutions (which are symplectic involutions induced by a translation by a 2-torsion section on an elliptic fibration) on such a surface. Each van Geemen–Sarti involution induces a 2-isogeny between two K3 surfaces, which is described in this paper.
Van Geemen-Sarti involutions and elliptic fibrations on K3 surfaces double cover of P2 / P. Comparin, A. Garbagnati. - In: JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN. - ISSN 0025-5645. - Vol. 66:2(2014 Apr), pp. 479-522.
|Titolo:||Van Geemen-Sarti involutions and elliptic fibrations on K3 surfaces double cover of P2|
|Parole Chiave:||Automorphisms of K3 surfaces; Elliptic fibrations; Isogenies; K3 surfaces; Symplectic involutions; Van Geemen-Sarti involutions|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||apr-2014|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.2969/jmsj/06620479|
|Appare nelle tipologie:||01 - Articolo su periodico|