Year: 2013
Type: preprint
Abstract: We give a way of estimating quickly the length of the hyperbolic isometry associated to a plane Cremona transformation that is presented as the product of two involutions. We also show, using the ideas of Cantat and Lamy, that, provided that the ground field is either algebraic of characteristic not 2 or of characteristic zero, the normal closure of a high power of such a transformation is a proper subgroup of the Cremona group; this gives an effective instantiation of some of their results. Moreover, we show that any hyperbolic Cremona transformation is rigid and give a simple criterion for it to be tight. This version is thoroughly revised from the previous version. In particular, it corrects an error in an earlier version that was pointed out by Lonjou.
Source: arXiv (Cornell University)
Author: Shepherd-Barron, N. I.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1502742186