Quantum cohomology of the Hilbert scheme of points in the plane

摘要

We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points of a",(2). 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.