Finite subgroups of the birational automorphism group are `almost' nilpotent

Attila Guld

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arXiv · 1903.07206

Finite subgroups of the birational automorphism group are `almost' nilpotent

Attila Guld

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Abstract

We call a group $G$ nilpotently Jordan of class at most $c$ $(c\in\mathbb{N})$ if there exists a constant $J\in\mathbb{Z}^+$ such that every finite subgroup $H\leqq G$ contains a nilpotent subgroup $K\leqq H$ of class at most $c$ and index at most $J$. We show that the birational automorphism group of a $d$ dimensional variety over a field of characteristic zero is nilpotently Jordan of class at most $d$.

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Attila Guld. 2019-03-18. Finite subgroups of the birational automorphism group are `almost' nilpotent. https://arxiv.org/abs/1903.07206

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