The quantum differential equation of the Hilbert scheme of points in the plane

Abstract

We discuss here basic properties of the quantum differential equation of the Hilbert scheme of points in the plane. Our emphasis is on intertwining operators (which shift equivariant parameters) and their applications. In particular, we obtain an exact solution to the connection problem from the Donaldson-Thomas point q=0 to the Gromov-Witten point q=-1. The paper is an expanded version of what was once the last Section of arXiv:math/0411210.

Final version from 2010

References in corpus (2)

• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds

Cited by in corpus (1)

• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics