Actions of Cremona groups on CAT(0) cube complexes

Autor:	Lonjou, Anne, Urech, Christian
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Group Theory 14E07 20F65 20F67
Druh dokumentu:	Working Paper
Popis:	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. Comment: Various small changes suggested by the referee. Accepted for publication in the Duke Mathematical Journal
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.00783 Zobrazit plný text záznamu View this record from Arxiv