A birationality result for character varieties
Geometric Topology
2015-08-20 v2
Abstract
Let M be an orientable, cusped hyperbolic 3-manifold of finite volume. We show that the restriction map from a Dehn surgery component in the PSL(2,C)-character variety of M to the character variety of the boundary of M is a birational isomorphism onto its image. This generalises a result by Nathan Dunfield. A key step in our proof is the exactness of Craig Hodgson's volume differential on the eigenvalue variety.
Keywords
Cite
@article{arxiv.1309.6010,
title = {A birationality result for character varieties},
author = {Ben Klaff and Stephan Tillmann},
journal= {arXiv preprint arXiv:1309.6010},
year = {2015}
}
Comments
8 pages; minor corrections in light of referee's comments; to appear in Mathematical Research Letters