NoetherLefschetz locus on singular threefolds
NoetherLefschetz locus on singular threefolds

Antonella Grassi, UPenn
Fine Hall 322
The classical NoetherLefschetz theorem says that any curve in a very general surface X in P^3 of degree d \geq 4 is a restriction of a surface in the ambient space, in particular the Picard number of X is 1 (a property is very general if it holds in the complement of countably many proper closed subvarieties).The NoetherLefschetz locus S_d is the locus of the degree d \geq 4 surfaces in P^3 whose Picard number is greater than 1. I will discuss
generalizations and applications to singular ambient spaces, and also
in particular properties of the components of maximal codimension in the NoetherLefschetz locus. (Base on work with Bruzzo and Lopez)