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.
Van Geemen-Sarti involutions and elliptic fibrations on K3 surfaces double cover of P2
A. Garbagnati
2014
Abstract
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.Pubblicazioni consigliate
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