Graduate Algebraic Geometry Seminar
Alexander Stathis
University of Illinois at Chicago
A Tiny Step Towards Schubert Calculus on the Hilbert Scheme of Points in P2
Abstract: The Grassmannian $G(k,n)$ of $k$-planes in an $n$-dimensional vector space $V$ has a basis for the
Chow ring given by the classes of the closures of "Schubert cells". These Schubert cells are indexed and defined
by Young tableaux with no more than $k$ rows and $n-k$ boxes per row. Furthermore, the intersection product
can be computed using a set of combinatorial identities involving the Young tableaux. This is known as
Schubert calculus. I'll talk about my recent work in attempting to provide an analog of Schubert calculus
for the Hilbert scheme of $n$ points in the projective plane $\mathbb{P}^2$. I'll describe the combinatorial
basis and show a method for computing intersection products of cycles with complementary codimension.
Wednesday September 23, 2015 at 3:00 PM in SEO 712