Boundedness results for singular Fano varieties and applications to Cremona groups
Algebraic Geometry
2021-02-02 v3
Abstract
This survey paper reports on work of Birkar, who confirmed a long-standing conjecture of Alexeev and Borisov-Borisov: Fano varieties with mild singularities form a bounded family once their dimension is fixed. Following Prokhorov-Shramov, we explain how this boundedness result implies that birational automorphism groups of projective spaces satisfy the Jordan property, answering a question of Serre in the positive.
Keywords
Cite
@article{arxiv.1812.04506,
title = {Boundedness results for singular Fano varieties and applications to Cremona groups},
author = {Stefan Kebekus},
journal= {arXiv preprint arXiv:1812.04506},
year = {2021}
}
Comments
Final version. To appear in the proceedings of the January 2019 edition of the S\'eminaire Nicolas Bourbaki