Actions of Cremona groups on CAT(0) cube complexes
Algebraic Geometry
2021-06-21 v2 Group Theory
Abstract
For each d we construct CAT(0) cube complexes on which Cremona groups rank d act by isometries. From these actions we deduce new and old group theoretical and dynamical results about Cremona groups. In particular, we study the dynamical behaviour of the irreducible components of exceptional loci, we prove regularization theorems, we find new constraints on the degree growth for non-regularizable birational transformations, and we show that the centralizer of certain birational transformations is small.
Keywords
Cite
@article{arxiv.2001.00783,
title = {Actions of Cremona groups on CAT(0) cube complexes},
author = {Anne Lonjou and Christian Urech},
journal= {arXiv preprint arXiv:2001.00783},
year = {2021}
}
Comments
Various small changes suggested by the referee. Accepted for publication in the Duke Mathematical Journal