Boundedness properties of automorphism groups of forms of flag varieties

2018/06/14 by Guld, Attila
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.05400

Abstract

We call a flag variety admissible if its automorphism group is the projective general linear group. (This holds in most cases.) Let K be a field of characteristic 0, containing all roots of unity. Let the K-variety X be a form of an admissible flag variety. We prove that X is either ruled, or the automorphism group of X is bounded, meaning that, there exists a constant C∈ℕ such that if G is a finite subgroup of Aut_K(X), then the cardinality of G is smaller than C.

Related

• Bound of automorphisms of projective varieties of general type
• Examples of authmorphism groups of ind-varieties of generalized flags
• Good reduction of algebraic groups and flag varieties
• Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics
• Realisation of abelian varieties as automorphism groups