# Chern classes of tautological sheaves on Hilbert schemes of points on surfaces

@article{Lehn1998ChernCO, title={Chern classes of tautological sheaves on Hilbert schemes of points on surfaces}, author={Manfred Lehn}, journal={Inventiones mathematicae}, year={1998}, volume={136}, pages={157-207} }

Abstract. We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on a smooth surface within the framework of Nakajima's oscillator algebra. This leads to an identification of the cohomology ring of Hilbn(A2) with a ring of explicitly given differential operators on a Fock space. We end with the computation of the top Segre classes of tautological bundles associated to line bundles on Hilbn up to n=7, extending…

## 248 Citations

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