The Picard lattice of a family of double covers of P^2
Dino Festi (Leiden)
What 


When 
Jan 14, 2016 from 01:00 pm to 02:00 pm 
Where  Mainz, 05432 (Hilbertraum) 
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A K3 surface is a smooth projective surface with trivial canonical divisor and trivial first cohomology group. A double cover of P^2 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 NéronSeveri) 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 I consider a 1dimensional family of K3 surfaces that are double covers of P^2 ramified along an almost diagonal sextic, and I am going to show how we computed the Picard lattice of the generic member of the family. This is a joint work with Florian Bouyer, Edgar Costa, Chris Nicholls, Isabel Vogt, and Mckenzie West.