The tame automorphism group of an affine quadric threefold acting on a square complex
Group Theory
2018-05-16 v3 Algebraic Geometry
Abstract
We study the group Tame(SL) of tame automorphisms of a smooth affine 3-dimensional quadric, which we can view as the underlying variety of SL(2,). We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is CAT(0) and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in Tame(SL) is linearizable, and that Tame(SL) satisfies the Tits alternative.
Keywords
Cite
@article{arxiv.1312.6153,
title = {The tame automorphism group of an affine quadric threefold acting on a square complex},
author = {Cinzia Bisi and Jean-Philippe Furter and Stéphane Lamy},
journal= {arXiv preprint arXiv:1312.6153},
year = {2018}
}
Comments
Minor correction at the end of 6.2.1, and perfect figures!