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Abstract des Vortrages von Paola Comparin

Van Geemen-Sarti involutions and elliptic fibrations on K3 surfaces

Let X be a K3 surface and E be an elliptic fibration on X. A van Geemen-Sarti involution on X is obtained as translation by a 2-torsion section of E. It is a symplectic involution and induces a 2-isogeny of K3 surfaces. I will report on a joint work with A. Garbagnati where we classified all van Geemen-Sarti involutions on K3 surfaces obtained as double covering of a blow up of P^2 branched along rational curves. The strategy to find all van Geemen-Sarti involutions consists in classifying the elliptic fibrations in order to analyse whether they admit a 2-torsion section. Moreover, I will show an explicit method which allows to obtain explicitly an equation for the elliptic fibration.