Some isogenies between complex K3 surfaces

Chiara Camere
(Universita' di Genova)

Abstract: The aim of this talk is to construct special isogenies between K3 surfaces, obtained by following quotients by symplectic automorphisms, and to determine the families of K3 surfaces for which this construction is possible. To this purpose we will prove that there are families of K3 surfaces of large dimension which both admit a finite symplectic automorphism and are desingularization of quotients of other K3 surfaces by a symplectic automorphism. In the second part of the talk we will consider the special case of involutions, and exhibit infinitely many sets of infinitely many K3 surfaces which are isogenous to each other. This is joint work in progress with A. Garbagnati.