Heisenberg Algebra and Hilbert Schemes of Points on Projective Surfaces

1997/03/01 by Hiraku Nakajima · 7 citations
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · doi:10.2307/2951818

openalex publication_date 1997/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

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 people (see e.g., [I, ES, Gö1, Gö2]). The other is the infinite dimensional Heisenberg algebra which is closely related to affine Lie algebras

Citations

• Algebraic Families on an Algebraic Surface
• Instantons and affine algebras I: The Hilbert scheme and vertex operators

Cited by

• Topological field theory and second-quantized five-branes
• A projection formula for the ind-Grassmannian
• Two point extremal Gromov-Witten invariants of Hilbert schemes of points on surfaces
• Recovering the good component of the Hilbert scheme
• Bases of representations of type A affine Lie algebras via quiver varieties and statistical mechanics
• Instanton counting with a surface operator and the chain-saw quiver
• Balanced Topological Field Theories
• The Chow Groups and the Motive of the Hilbert Scheme of Points on a Surface
• Hiraku Nakajima [wikipedia]