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

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.