Quantum cohomology of the Hilbert scheme of points in the plane

Abstract

We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points in the complex plane. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum Calogero-Sutherland many-body system. A relationship between the quantum cohomology of the Hilbert scheme and the Gromov-Witten/Donaldson-Thomas correspondence for local curves is proven.

arXiv commentRevised version. Results related to Jack symmetric functions moved to an upcoming paper

References in corpus (2)

• Hilbert schemes, Hecke algebras and the Calogero-Sutherland system
• Gromov-Witten invariants of the Hilbert scheme of 3-points on P^2

Cited by in corpus (10)

• Supersymmetric vacua and Bethe ansatz
• Gromov-Witten invariants of varieties with holomorphic 2-forms
• The Stringy Instanton Partition Function
• Random surfaces enumerating algebraic curves
• Vertex Operators and Moduli Spaces of Sheaves
• Donaldson-Thomas theory of A_n x P^1
• New calculations in Gromov-Witten theory
• The quantum differential equation of the Hilbert scheme of points in the plane
• A projection formula for the ind-Grassmannian
• Stringy Instanton Counting and Topological Strings