Families of commuting automorphisms, and a characterization of the affine space

2019/12/03 by Cantat, Serge, Regeta, Andriy, Xie, Junyi · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.01567

Abstract

In this paper we show that an affine space is determined by the abstract group structure of its group of regular automorphisms in the category of connected affine varieties. To prove this we study commutative subgroups of the group of automorphisms of affine varieties.

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• Borel subalgebras of Lie algebras of vector fields
• Borel subgroups of the automorphism groups of affine toric surfaces

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