Chern Classes of Tautological Sheaves on Hilbert Schemes

Details Chern Classes of Tautological Sheaves on Hilbert Schemes Chern Classes of Tautological Sheaves on Hilbert Schemes

1998-03-20

arxiv.org/abs/math/9803091v1

Mathematics

Algebraic Geometry

45 pages, LaTeX

Scientific paper

10.1007/s002220050307

We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification of the cohomology ring of Hilbert schemes of the affine plane with a ring of differential operators on a Fock space. We end with the computation of the top Segre classes of tautological bundles associated to line bundles on Hilb^n up to n=7, and give a conjecture for the generating series.

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