Seminários de Geometria Algébrica - The Noether-Lefschetz problem for normal varieties and the Hodge conjecture

Nome: 
Ugo Bruzzo (SISSA, Itália)
Instituição: 
Escola Internacional Superior de Estudos Avançados
Data do Evento: 
quinta-feira, 08 de Fevereiro de 2018 - 11:00
Local do evento
Sala 221
Descrição: 

The classical Noether-Lefschetz problem is about the Picard number of surfaces in P3. For d > 3, if S(d) is the locus of smooth surfaces in the linear system O(d) on P3, the very general surface in S(d) has Picard number one. It is possible to estimate the codimensions of the components of S(d), and show that their codimension is related to geometric properties of the surfaces they describe. Over the last few years, in collaboration with A. Grassi, and more recently with A.F. Lopez, I have investigated generalizations to surfaces in normal, Q-factorial 3-folds. My talk will be devoted to describe some of the results we obtained. I will also describe an application which provides a proof of the Hodge conjecture for hypersurfaces in toric varieties.