Root Systems and the Quantum Cohomology of ADE resolutions
Algebraic Geometry
2007-07-12 v1 High Energy Physics - Theory
Quantum Algebra
Abstract
We compute the C*-equivariant quantum cohomology ring of Y, the minimal resolution of the DuVal singularity C^2/G where G is a finite subgroup of SU(2). The quantum product is expressed in terms of an ADE root system canonically associated to G. We generalize the resulting Frobenius manifold to non-simply laced root systems to obtain an n parameter family of algebra structures on the affine root lattice of any root system. Using the Crepant Resolution Conjecture, we obtain a prediction for the orbifold Gromov-Witten potential of [C^2/G].
Keywords
Cite
@article{arxiv.0707.1337,
title = {Root Systems and the Quantum Cohomology of ADE resolutions},
author = {Jim Bryan and Amin Gholampour},
journal= {arXiv preprint arXiv:0707.1337},
year = {2007}
}