Alexander Stathis : A Tiny Step Towards Schubert Calculus on the Hilbert Scheme of Points in P2

Posted by Alex Stathis , part of the Graduate Algebraic Geometry Seminar.

At

Sept. 23, 2015, 3 p.m.

In

SEO 712

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.