turkmath.org

A K3 surface is a smooth projective surface with trivial canonical divisor and trivial first cohomology group. A double cover of P2 ramified along a smooth sextic curve is an example of K3 surface. To every K3 surface it is possible to associate a lattice, called Picard (or N ́eron-Severi) lattice. The Picard lattice encodes important information about the arithmetic and the geometry of the surface, and it is often not easy to compute. In this talk we will consider a 1-dimensional family of K3 surfaces that are double covers of P2 ramified along an almost diagonal sextic, and we will see how we can compute the Picard lattice of the generic member of the family. This is a joint work with Florian Bouyer, Edgar Costa, Chris Nicholls, and Mckenzie West.