Braid groups and Kleinian singularities
Algebraic Geometry
2010-06-07 v3 Quantum Algebra
Representation Theory
Abstract
We establish faithfulness of braid group actions generated by twists along an ADE configuration of -spherical objects in a derived category. Our major tool is the Garside structure on braid groups of type ADE. This faithfulness result provides the missing ingredient in Bridgeland's description of a space of stability conditions associated to a Kleinian singularity.
Keywords
Cite
@article{arxiv.0910.2521,
title = {Braid groups and Kleinian singularities},
author = {Christopher Brav and Hugh Thomas},
journal= {arXiv preprint arXiv:0910.2521},
year = {2010}
}
Comments
Section 4 from versions 1 and 2 has been deleted due to an error in the proof of Theorem 2. Renamed the paper and rewrote the other sections to reflect this change