Seminário de Geometria Algébrica: Noether-Lefschetz theory for P^3 and Mori dream spaces.

Abstract: In this talk, I will give a brief introduction to the Noether-Lefschetz theory in the 3-dimensional projective space over the complex numbers which deals with smooth surfaces with degree bigger than or equal to 4 and whose Picard rank (Picard number) is strictly bigger than 1. Then, I will introduce Mori dream spaces using the Cox ring. Finally, I will show a connection between these two theories via K3 surfaces with Picard number 2. This is a joint work in progress with Antonio Laface and Alex Massarenti.