Van Geemen--Sarti involutions and elliptic fibrations on K3 surfaces double cover of $\mathbb{P}^2$

Details Van Geemen--Sarti involutions and elliptic fibrations on K3 surfaces double cover of $\mathbb{P}^2$ Van Geemen--Sarti involutions and elliptic fibrations on K3 surfaces double cover of $\mathbb{P}^2$

2011-10-28

arxiv.org/abs/1110.6380v1

Mathematics

Algebraic Geometry

36 pages

Scientific paper

In this paper we classify the elliptic fibrations on K3 surfaces which are the double cover of a blow up of $\mathbb{P}^2$ 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.

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