Article

Inventiones mathematicae

, Volume 179, Issue 3, pp 523-557

First online:

Quantum cohomology of the Hilbert scheme of points in the plane

  • A. OkounkovAffiliated withDepartment of Mathematics, Princeton University Email author 
  • , R. PandharipandeAffiliated withDepartment of Mathematics, Princeton University

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Abstract

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.