Finite $p$-groups of birational automorphisms and characterizations of rational varieties

Jinsong Xu

Finite $p$-groups of birational automorphisms and characterizations of rational varieties

Algebraic Geometry 2018-09-26 v1

Authors: Jinsong Xu

Abstract

We study finite $p$ -subgroups of birational automorphism groups. By virtue of boundedness theorem of Fano varieties, we prove that there exists a constant $R(n)$ such that a rationally connected variety of dimension $n$ over an algebraically closed field is rational if its birational automorphism group contains a $p$ -subgroups of maximal rank for $p > R(n)$ . Some related applications on Jordan property are discussed.

Keywords

finite p-groups birational automorphisms rationally connected varieties fano varieties jordan property rational varieties

Cite

@article{arxiv.1809.09506,
  title  = {Finite $p$-groups of birational automorphisms and characterizations of rational varieties},
  author = {Jinsong Xu},
  journal= {arXiv preprint arXiv:1809.09506},
  year   = {2018}
}

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