English

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

R2 v1 2026-06-22T01:32:40.868Z