JP Journal of Geometry and Topology
Volume 8, Issue 1, Pages 7 - 21
(March 2008)
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CHARACTERISTIC CLASSES OF THE HILBERT SCHEMES OF POINTS ON NON-COMPACT SIMPLY-CONNECTED SURFACES
Marc A. Nieper-Wisskirchen (Germany)
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Abstract:
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. |
| Keywords and phrases: Hilbert scheme, characteristic classes, equivariant cohomology, universal formulas, Lagrange-Good formula. |
| Communicated by Yasuo Matsushita |
| Number of Downloads: 256 | Number of Views: 802 |
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