LGRT 1681
Solomon Lefschetz showed that the Picard group of a general surface in ℙ3𝑃3 of degree greater than 3 is ℤ𝑍. That is, the vast majority of surfaces in ℙ3𝑃3 have the smallest possible Picard group. The set of surfaces of degree greater than 3 on which this theorem fails is called the Noether-Lefschetz locus. This locus has infinitely many components and their dimensions are still somehow mysterious.
In this talk, I will calculate the dimension of infinitely many components of the Noether-Lefschetz locus. These components are simple to describe and give us an idea of the complexity of the entire Noether-Lefschetz locus. This is joint work with Montserrat Vite and Manuel Leal.
Note:
Refreshments at 3:45PM.