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

2019/03/18 by Attila Guld, Guld, Attila
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1903.07206

openalex publication_date 2019/03/18 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

We call a group G nilpotently Jordan of class at most c (c∈ℕ) if there exists a constant J∈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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