turkmath.org

We will continue the subject of the previous talks, viz. a characterization of the K3-surfaces covering an Enriques surface. Following Nikulin, we will: (1) explain that the existence of a fixed point free involution depends on the *genus* of the transcendental lattice only; (2) give the answer for *most* genera, leaving just a few of them open; (3) outline the difficulties that may arise in the case of those few open genera. (4) determine the complete list of genera of positive definite lattices of arbitrary rank each of whose members represents 1 for rank different from 2 and 3. As an application, we classify K3 surfaces which do not cover any Enriques surface. This is joint work with SIMON BRANDHORST, DAVIDE CESARE VENIANI.