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Noether-Lefschetz loci formed by determinantal surfaces in projective 3-space.

Event Category:
Valley Geometry Seminar
César Lozano Huerta
Universidad Nacional Autónoma de México, Oaxaca

Solomon Lefschetz showed that the Picard group of a general surface in ${\mathbb P}^3$ of degree greater than 3 is $\mathbb Z$. That is, the vast majority of surfaces in ${\mathbb P}^3$ 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.

Friday, December 1, 2023 - 4:00pm
LGRT 1681

Refreshments at 3:45PM.