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

Jinsong Xu

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arXiv · 1809.09506

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

Jinsong Xu

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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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BibTeX RIS

Jinsong Xu. 2018-09-25. Finite $p$-groups of birational automorphisms and characterizations of rational varieties. https://arxiv.org/abs/1809.09506

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