Algebraic Geometry Seminar
Wednesday January 29th, 2020
Time: 4:00 PM - 5:30 PM
Title: Continuous families of divisors on symmetric powers of curves
Speaker: John Sheridan, Stony Brook University
Abstract:
For $X$ a smooth projective variety, we consider its set of effective divisors in a fixed cohomology class. This set naturally forms a projective scheme and if $X$ is a curve, this scheme is a smooth, irreducible variety (fibered in linear systems over the Picard variety). However, when $X$ is of higher dimension, this scheme can be singular and reducible. We study its structure explicitly when $X$ is a symmetric power of a curve.