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

Cesar Lozano Huerta, from U. Oaxaca/ Harvard

Abstract:

Surfaces in projective 3-space are simple in many respects, but they still allow us a glance of the complexity of all surfaces.

S. Lefschetz proved that the Picard group of a general surface in P3 of degree d is ZZ. That is, the vast majority of smooth surfaces in P3 have the smallest possible Picard group. The set of surfaces for which this theorem fails is called the Noether-Lefschetz locus and has infinitely many components whose dimensions are somehow mysterious.

In this talk, I will compute the dimension of infinitely many Noether-Lefschetz components which are simple in some sense, but they still give us an idea of the complexity of the entire Noether-Lefschetz locus. This is joint work with Montserrat Vite and Manuel Leal.

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