Finite subgroups of the birational automorphism group are 'almost'\n nilpotent of class at most two

2020/04/22 by Attila Guld, Guld, Attila
Computer Science · Mathematics · Social Sciences · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research #Migration, Ethnicity, and Economy

paper · pdf · doi:10.48550/arxiv.2004.11715

openalex publication_date 2020/04/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We call a group G nilpotently Jordan of class at most c\n(c\∈\ℕ) if there exists a constant J\∈\ℤ⁺ such that\nevery finite subgroup H leqq G contains a nilpotent subgroup K leqq H of\nclass at most c and index at most J. We show that the birational\nautomorphism group of a variety over a field of characteristic zero is\nnilpotently Jordan of class at most two.\n

Citations

• Diffeomorphism Groups of Compact 4-manifolds are not always Jordan
• Lectures on birational geometry

Related

• Finite subgroups of the birational automorphism group are `almost' nilpotent
• Jordan properties of automorphism groups of certain open algebraic varieties
• Constructing Highly Symmetric Compact Manifolds and Algebraic Varieties
• Almost nilpotency of an associative algebra with an almost nilpotent\n fixed-point subalgebra
• Jordan groups, conic bundles and abelian varieties