Characteristic classes of the Hilbert schemes of points on non-compact simply-connected surfaces
Abstract
Description
We prove a closed formula expressing any multiplicative characteristic class evaluated on the tangent bundle of the Hilbert schemes of points on a non-compact simply-connected surface.
As a corollary, we deduce a closed formula for the Chern character of the tangent bundles of these Hilbert schemes.
We also give a closed formula for the multiplicative characteristic classes of the tautological bundles associated to a line bundle on the surface.
We finally remark which implications the results here have for the Hilbert schemes of points of an arbitrary surface.
8 pages
8 pages