English

Automorphism groups of almost homogeneous varieties

Algebraic Geometry 2019-11-21 v2

Abstract

Consider a smooth connected algebraic group GG acting on a normal projective variety XX with an open dense orbit. We show that Aut(XX) is a linear algebraic group if so is GG; for an arbitrary GG, the group of components of Aut(XX) is arithmetic. Along the way, we obtain a restrictive condition for GG to be the full automorphism group of some normal projective variety.

Keywords

Cite

@article{arxiv.1810.09115,
  title  = {Automorphism groups of almost homogeneous varieties},
  author = {Michel Brion},
  journal= {arXiv preprint arXiv:1810.09115},
  year   = {2019}
}

Comments

Revised version, substantial changes in Section 2. To appear in a volume in honor of Bill Fulton

R2 v1 2026-06-23T04:47:49.951Z