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}
}
  • M. Lehn
  • Published 20 March 1998
  • Mathematics
  • Inventiones mathematicae
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… 
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