双有理群与伪自同构群的公度作用
代数几何
2020-02-18 v3 群论
几何拓扑
摘要
伪自同构是在余维数1上作为正则自同构作用的双有理变换。我们引入几何群论的思想来证明，一个在CAT(0)立方复形上满足不动点性质的双有理变换群（例如具有Kazhdan性质(T)的离散可数群）在双有理意义下共轭于一个在某个非空Zariski开子集上通过伪自同构作用的群。我们应用这一论证来分类具有此不动点性质的曲面双有理变换群，直至双有理共轭。
引用
@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}
}
备注
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