Some automorphism groups are linear algebraic

2019/12/15 by Brion, Michel
#14L30 #14M17 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.06985

Abstract

Consider a normal projective variety X, a linear algebraic subgroup G of Aut(X), and the field K of G-invariant rational functions on X. We show that the subgroup of Aut(X) that fixes K pointwise is linear algebraic. If K has transcendence degree 1 over k, then Aut(X) is an algebraic group.

Related

• Automorphism groups of almost homogeneous varieties
• When is the automorphism group of an affine variety linear?
• Realisation of linear algebraic groups as automorphism groups
• Automorphism groups of finite dimensional simple algebras
• On algebraic automorphisms and their rational invariants