# Homology of Hilbert schemes of points on a locally planar curve

```@article{Rennemo2013HomologyOH,
title={Homology of Hilbert schemes of points on a locally planar curve},
author={J. Rennemo},
journal={arXiv: Algebraic Geometry},
year={2013}
}```
• J. Rennemo
• Published 2013
• Mathematics
• arXiv: Algebraic Geometry
Let C be a proper, integral, locally planar curve, and consider its Hilbert schemes of points C^[n]. We define 4 creation/annihilation operators acting on the rational homology groups of these Hilbert schemes and show that the operators satisfy the relations of a Weyl algebra. The action of this algebra is similar to that defined by Grojnowski and Nakajima for a smooth surface. As a corollary, we compute the cohomology of C^[n] in terms of the cohomology of the compactified Jacobian of C… Expand
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#### References

SHOWING 1-10 OF 18 REFERENCES
A support theorem for Hilbert schemes of planar curves
• Mathematics
• 2013
Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that theExpand
Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation
• V. Shende
• Mathematics
• Compositio Mathematica
• 2012
Abstract Let C be a locally planar curve. Its versal deformation admits a stratification by the genera of the fibres. The strata are singular; we show that their multiplicities at the central pointExpand
Macdonald formula for curves with planar singularities
• Mathematics
• 2011
We generalize Macdonald's formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes toExpand
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 variousExpand
Algebraic cycles on the relative symmetric powers and on the relative Jacobian of a family of curves. I
Abstract.In this paper we construct and study the actions of certain deformations of the Lie algebra of Hamiltonians on the plane on the Chow groups (resp., cohomology) of the relative symmetricExpand
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 generalisesExpand
13/2 ways to count curves
• Mathematics, Physics
• 2011
In the past 20 years, compactifications of the families of curves in algebraic varieties X have been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable quotients.Expand
An intersection number for the punctual Hilbert scheme of a surface
• Mathematics
• 1996
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.Expand
Stable pairs and BPS invariants
• Mathematics, Physics
• 2007
We define the BPS invariants of Gopakumar-Vafa in the case of irreducible curve classes on Calabi-Yau 3-folds. The main tools are the theory of stable pairs in the derived category and Behrend'sExpand
CELLULAR DECOMPOSITIONS FOR NESTED HILBERT SCHEMES OF POINTS
where the symbol n is used as a shorthand for the m-tuple (n1, n2, .., nm). This shorthand will be used throughout the paper. There is, of course, no loss of generality in assuming that n1 < n2 < ...Expand