Continuous automorphisms of Cremona groups
Algebraic Geometry
2019-09-25 v1 Group Theory
Abstract
We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show that a similar result holds if we consider groups of polynomial automorphisms of affine spaces instead of Cremona groups.
Keywords
Cite
@article{arxiv.1909.11050,
title = {Continuous automorphisms of Cremona groups},
author = {Christian Urech and Susanna Zimmermann},
journal= {arXiv preprint arXiv:1909.11050},
year = {2019}
}