Eric Larson : THE SEMINAR IS CANCELLED

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Jan. 19, 2024, 11 a.m.

In

636 SEO

Abstract

By Bezout's theorem, a space curve of degree d intersects a quadric Q in 2d points. The dimensions of the Hilbert schemes of Brill--Noether space curves of degree d and genus g, and of 2d points on Q, are both of dimension 4d. It is therefore natural to expect that intersecting with a quadric induces an etale map between these Hilbert schemes. In characteristic zero, this is the case with exactly 6 exceptions. This talk will focus on understanding what happens in characteristic 2, and in particular, why the analogous statement fails in a dramatic way.