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.

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

Cited by in corpus (2)

• Regularization of birational actions of FW groups
• Property FW, differentiable structures, and smoothability of singular actions