turkmath.org

I will continue the subject of the previous talks, viz. a characterization of the K3-surfaces covering an Enriques surface. I 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. (Following Nikulin, we describe the genus of an even lattice by means of its signature and discriminant form; for small ranks, the relevant data, viz. length and parity of the 2-primary part, can be restated in terms of the parity of the coefficients of the Gram matrix.)