Commensurating actions of birational groups and groups of pseudo-automorphisms
Abstract
Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on CAT(0) cubical complexes, for example a discrete countable group with Kazhdan Property (T), is birationally conjugate to a group acting by pseudo-automorphisms on some non-empty Zariski-open subset. We apply this argument to classify groups of birational transformations of surfaces with this fixed point property up to birational conjugacy.
Keywords
Cite
@article{arxiv.1704.02043,
title = {Commensurating actions of birational groups and groups of pseudo-automorphisms},
author = {Serge Cantat and Yves de Cornulier},
journal= {arXiv preprint arXiv:1704.02043},
year = {2020}
}
Comments
V1 was a preliminary version. V1->V2: significantly expanded version with new sections. V2->V3: various corrections, and removal of the whole "categorical limit construction" section, now bypassed using divisorial valuations. 49 pages, 3 figures