Vertex algebras and the cohomology ring structure of Hilbert schemes of points on surfaces

By Wei-Ping Li, Zhenbo Qin, Weiqiang Wang. 2000

83 citations recorded by the source corpus.

Abstract. 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 of complex numbers.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f31e511abba03611ead329d265d1389d65414234

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

The cup product of Hilbert schemes for K3 surfaces (2003, methodology): “The following proposition was first proved by the first named author [14, Thm 4.2] for the special case α = ch(F), F a locally free sheaf on X, and then extended to the general case by Li, Qin and Wang [16]: Theorem 3.6.”
INTEGRAL CONSTRAINTS ON THE MONODROMY GROUP OF THE HYPERKÄHLER RESOLUTION OF A SYMMETRIC PRODUCT OF A K3 SURFACE (2006, background): “en in equation (17). 2. The cohomology group Hi(M,Z) vanishes, for odd i, and is torsion free, when iis even. 13 Generators for the cohomology ring H∗(X[n],Q), with rational coeﬃcients, were found in [LQW] for any projective surface X. A basis for the group H∗(X[n],Z)/torsion is given in [QW] for ma”
Orbifold cohomology for global quotients (2001, result): “ of S[n] has been explicitly computed by Lehn and Sorger [LS2] for a surface S with trivial c1(TS) (building on previous results of Nakajima [N1], [N2], Grojnowski [Gr], Lehn [L] and Li, Qin and Wang [LQW]). This paper started as an attempt to verify Chen and Ruan’s conjecture using the result of Le”
Quantum cohomology of the Hilbert scheme of points in the plane (2004, background): “The T -equivariant cohomology of Hilbn has been recently determined, see [6, 17, 18, 19, 34].”
The cup product of the Hilbert scheme for K3 surfaces (2000, background): “A G ] 1 8 D ec of generalised n-tuples of any smooth projective surface X with trivial canonical bundle.”
The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces (2010, unknown): “→ηi H2i(M) → H2i(M) is surjective, for all i≥ 1. Proof. The subspaces chi(φ′(K(S)), i ≥ 1, generate the cohomology ring H∗(M), by ([Ma1], Corollary 2). When M = S[n], this was proven independently in [LQW]. The same statement holds for the subspaces chi(φ(K(S)). Indeed, ch1(φ(K(S)) = ch1(φ′(K(S)) = ”
The local Donaldson–Thomas theory of curves (2005, unknown): “ows D= − 2,1d−2 . The classical multiplication of Don the Fock space F is given by the following operator: −(t 1 +t 2) X k>0 k−1 2 α−kαk+ 1 2 X k,l>0 h t 1t 2 αk+lα−kα−l− α−k−lαkαl i , (45) see [13, 14, 16, 29]. The ﬁrst summand of (45) contains a term proportional to the energy operator, |·| ”