Automorphism groups of non-normal rigid affine surfaces are finite-dimensional

Ivan Beldiev; Alexander Perepechko

Automorphism groups of non-normal rigid affine surfaces are finite-dimensional

Algebraic Geometry 2026-07-01 v1

Authors: Ivan Beldiev , Alexander Perepechko

Abstract

It was recently established by Perepechko and Zaidenberg that the automorphism group of a normal affine surface is finite-dimensional if and only if the surface admits no non-trivial action of the additive group of the base field. We extend this result to non-normal affine surfaces.

Keywords

automorphism groups affine surfaces non-normal surfaces rigid surfaces finite-dimensional additive group action

Cite

@article{arxiv.2607.00652,
  title  = {Automorphism groups of non-normal rigid affine surfaces are finite-dimensional},
  author = {Ivan Beldiev and Alexander Perepechko},
  journal= {arXiv preprint arXiv:2607.00652},
  year   = {2026}
}