Abstract
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.
Citation
Paola COMPARIN. Alice GARBAGNATI. "Van Geemen-Sarti involutions and elliptic fibrations on $K3$ surfaces double cover of $\mathbb{P}^2$." J. Math. Soc. Japan 66 (2) 479 - 522, April, 2014. https://doi.org/10.2969/jmsj/06620479
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