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

2018/09/25 by Xu, Jinsong
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.09506

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.

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