Quantum cohomology of the Hilbert scheme of points in the plane
Algebraic Geometry
2008-04-15 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.math/0411210,
title = {Quantum cohomology of the Hilbert scheme of points in the plane},
author = {A. Okounkov and R. Pandharipande},
journal= {arXiv preprint arXiv:math/0411210},
year = {2008}
}
Comments
Revised version. Results related to Jack symmetric functions moved to an upcoming paper