209 citations · 1.5k across the 128 of their papers we have counts for
13 papers · 1 filter
Anti-commuting varieties
Xinhong Chen, Weiqiang Wang
We study the anti-commuting variety which consists of pairs of anti-commuting matrices. We provide an explicit description of its irreducible components and their dimen…
The cohomology rings of Hilbert schemes via Jack polynomials
Wei-Ping Li, Zhenbo Qin, Weiqiang Wang
In this note, generalizing earlier work of Nakajima and Vasserot, we study the (equivariant) cohomology rings of Hilbert schemes of certain toric surfaces and establish their conne…
Integral operators and integral cohomology classes of Hilbert schemes
Zhenbo Qin, Weiqiang Wang
The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of H…
Hilbert schemes, integrable hierarchies, and Gromov-Witten theory
Wei-Ping Li, Zhenbo Qin, Weiqiang Wang
Various equivariant intersection numbers on Hilbert schemes of points on the affine plane are computed, some of which are organized into tau-functions of 2-Toda hierarchies. A corr…
Ideals of the cohomology rings of Hilbert schemes and their applications
Wei-Ping Li, Zhenbo Qin, Weiqiang Wang
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…
Hilbert schemes and symmetric products: a dictionary
Zhenbo Qin, Weiqiang Wang
Given a closed complex manifold of even dimension, we develop a systematic (vertex) algebraic approach to study the rational orbifold cohomology rings $\orbsym$ of the symmetri…
Hilbert schemes and W algebras
Wei-Ping Li, Zhenbo Qin, Weiqiang Wang
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…
Stability of the cohomology rings of Hilbert schemes of points on surfaces
Wei-Ping Li, Zhenbo Qin, Weiqiang Wang
We establish some remarkable properties of the cohomology rings of the Hilbert schemes of n points on a projective surface X, from which one sees to what extent these cohomology ri…
Generators for the cohomology ring of Hilbert schemes of points on surfaces
Wei-ping Li, Zhenbo Qin, Weiqiang Wang
Using the methods developed in [LQW], math.AG/0009132, we obtain a second set of generators for the cohomology ring of the Hilbert scheme of points on an arbitrary smooth projectiv…
Vertex algebras and the cohomology ring structure of Hilbert schemes of points on surfaces
Wei-ping Li, Zhenbo Qin, Weiqiang Wang
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field…
Resolution of singularities of null cones
Weiqiang Wang
We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singula…
Orbifold Hodge numbers of the wreath product orbifolds
Weiqiang Wang, Jian Zhou
We prove that the wreath product orbifolds studied earlier by the first author provide a large class of higher dimensional examples of orbifolds whose orbifold Hodge numbers coinci…
Hilbert schemes, wreath products, and the McKay correspondence
Weiqiang Wang
Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-…