# Hilbert schemes and W algebras

@article{Li2001HilbertSA,
title={Hilbert schemes and W algebras},
author={Wei-Ping Li and Zhenbo Qin and Weiqiang Wang},
journal={arXiv: Algebraic Geometry},
year={2001}
}
• Published 5 November 2001
• Mathematics
• arXiv: Algebraic Geometry
We construct geometrically the generating fields of a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes of n points on a projective surface for all n. We compute explicitly the commutators among a set of linear basis elements of the W algebra, and identify this algebra with a $W_{1+\infty}$-type algebra. A precise formula of certain Chern character operators, which is essential for the construction of the W algebra, is established in terms of the…
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We study the ideals of the rational cohomology ring of the Hilbert scheme X (n) of n points on a smooth projective surface X. As an application, for a large class of smooth quasi-projective surfaces
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Given a closed complex manifold $X$ of even dimension, we develop a systematic (vertex) algebraic approach to study the rational orbifold cohomology rings $\orbsym$ of the symmetric products. We
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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
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Using the methods developed in [LQW], we obtain a second set of generators for the cohomology ring of the Hilbert scheme of points on an arbitrary smooth projective surface X over the field of
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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