A birationality result for character varieties

Ben Klaff; Stephan Tillmann

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arXiv · 1309.6010

A birationality result for character varieties

Ben Klaff·Stephan Tillmann

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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.

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Ben Klaff, Stephan Tillmann. 2013-09-24. A birationality result for character varieties. https://arxiv.org/abs/1309.6010

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