Inventiones mathematicae

, Volume 179, Issue 3, pp 523–557

Quantum cohomology of the Hilbert scheme of points in the plane


DOI: 10.1007/s00222-009-0223-5

Cite this article as:
Okounkov, A. & Pandharipande, R. Invent. math. (2010) 179: 523. doi:10.1007/s00222-009-0223-5


We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points of ℂ2. 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.

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© copyright by the authors 2009

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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