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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References

SHOWING 1-10 OF 31 REFERENCES

More lectures on Hilbert schemes of points on surfaces

This paper is based on author's lectures at Kyoto University in 2010 Summer, and in the 6th MSJ-SI `Development of Moduli Theory' at RIMS in June 2013. The purpose of lectures was to review several

Top Segre Class of a Standard Vector Bundle εD4 on the Hilbert Scheme Hilb4S of a Surface S

This work is a continuation of the paper [4] of the present collection. Using the results of [4] (and keeping the notations introduced there), we compute here the degree \({\delta _4} =

An intersection number for the punctual Hilbert scheme of a surface

We compute the intersection number between two cycles A and B of complementary dimensions in the Hilbert scheme H parameterizingr subschemes of given finite length n of a smooth projective surface S.

Bott’s formula and enumerative geometry

We outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic

The cohomology ring of the Hilbert scheme of 3 points on a smooth projective variety.

Let Xbe a smooth projective variety over the complex numbers C and X the Hubert scheme of subschemes of length 3 of JSf, which is known to be smooth. The additive structure of H* (P2, Z) has been

Instantons and affine algebras I: The Hilbert scheme and vertex operators

This is the first in a series of papers which describe the action of an affine Lie algebra with central charge $n$ on the moduli space of $U(n)$-instantons on a four manifold $X$. This generalises

The Betti numbers of the Hilbert scheme of points on a smooth projective surface

Several authors have been interested in the Hilbert scheme SPq:=Hilb"(S) parametrizing finite subschemes of length n on a smooth projective surface S. In EF 1] and I-F 2] Fogarty shows that S tnj is

Heisenberg algebra and Hilbert schemes of points on projective surfaces

The purpose of this paper is to throw a bridge between two seemingly unrelated subjects. One is the Hilbert scheme of points on projective surfaces, which has been intensively studied by various

On the homology of the Hilbert scheme of points in the plane

Geir Ellingsrud 1 and Stein Arild Stromme 2 i Matematisk institutt, Universitetet i Oslo, Blindern, N-Oslo 3, Norway 2 Matematisk institutt, Universitetet i Bergen, N-5014 Bergen, Norway Although

Linear Determinants with Applications to the Picard Scheme of a Family of Algebraic Curves

The linear determinant.- Representation of n-fold sections by symmetric products.- Invertible sheaves and rational maps into C(g).- Construction of the Picard scheme of a family of curves.