Raymond Cheng, Department of Pure Mathematics, University of Waterloo
“Poincar Polynomials of the Hilbert Scheme of Points”
So far, we have discussed a few topological properties of the Hilbert Scheme of points in the plane. Indeed, we have seen that it is nonsingular and connected, so irreducible as well. We now go a bit further and shall see something about the homology of the Hilbert scheme. Specifically, over the next little while, we will use some Morse theoretic techniques to compute the dimensions of the homology groups of the Hilbert scheme. This talk will represent the beginning of that endeavour: we will describe a Khler structure on the Hilbert scheme and talk a bit about Morse theory. We will also sketch how we will proceed from there.
MC 5403