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 computations of Severi, LeBarz, Tikhomirov and Troshina and give a conjecture for the generating series.
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Oblatum: 25-III-1998 & 17-VII-1998 / Published online: 28 January 1999
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Lehn, M. Chern classes of tautological sheaves on Hilbert schemes of points on surfaces. Invent math 136, 157–207 (1999). https://doi.org/10.1007/s002220050307
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DOI: https://doi.org/10.1007/s002220050307