Graduate Algebraic Geometry Seminar
Alexander Stathis
UIC
The Hilbert Scheme of Points on a Surface
Abstract: Let $X$ be a smooth projective surface, and fix a positive integer $n$. In this talk, we will follow the work of
Fogarty in "Algebraic Families on an Algebraic Surface" to show that ${Hilb}^n(X) := X^{[n]}$, the Hilbert scheme
parameterizing zero dimensional subschemes $Z \subset X$ of length $n$, is connected and smooth, and that the
Hilbert-Chow morphism $h : X^{[n]} \to X^{(n)}$, where $X^{(n)}$ is the $n$-th symmetric product of $X$, is birational.
Thursday October 10, 2013 at 3:30 PM in SEO 712