Quantum cohomology of the Hilbert scheme of points in the plane

2004/11/09 by Andreĭ Okounkov, Okounkov, A., Rahul Pandharipande +1 · 6 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0411210

openalex publication_date 2004/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points
• Gromov-Witten invariants of varieties with holomorphic 2-forms
• Donaldson-Thomas theory of A_n x P¹
• Random surfaces enumerating algebraic curves
• Gromov-Witten theory of Hilbⁿ(ℂ²) and Noether-Lefschetz theory of A_g
• Stringy Instanton Counting and Topological Strings

Related

• Quantum cohomology of the Hilbert scheme of points on an elliptic surface
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