Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane

Details Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane

2004-10-21

arxiv.org/abs/math/0410458v2

Mathematics

Algebraic Geometry

20 pages; to appear in J. Alg. Geom

Scientific paper

The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for the Chern classes of the tangent bundle over the Hilbert scheme of points on a projective surface. The second tool leads then to nice generating formulas in the particular case of the Hilbert scheme of points on the affine plane.

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