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

SEMINARS: HARVARD-MIT ALGEBRAIC GEOMETRY

When: November 21, 2023
3:00 pm - 4:00 pm
Where: Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138, United States
Speaker: César Lozano Huerta - Universidad Nacional Autónoma de México

Solomon Lefschetz showed that the Picard group of a general surface in P3 of degree greater than three is ZZ. That is, the vast majority of surfaces in P3 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 infinite components and their dimensions are somehow mysterious.

In this talk, I will calculate the dimension of infinite Noether-Lefschetz components that are simple in a sense, but still give us an idea of the complexity of the entire Noether-Lefschetz locus. This is joint work with Montserrat Vite and Manuel Leal.

For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar