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On Ramanujam's Theorem About Finite Dimensional Groups of Automorphisms

Algebraic Geometry 2026-05-15 v1 Group Theory

Abstract

Ramanujam's theorem states that any connected finite-dimensional subgroup of the automorphism group Aut(X)\mathrm{Aut}(X) of an irreducible variety XX is an algebraic group, in a natural way. In this note, we discuss the notion of dimension and extend Ramanujam's theorem to arbitrary (not necessarily irreducible) varieties.

Keywords

Cite

@article{arxiv.2605.13510,
  title  = {On Ramanujam's Theorem About Finite Dimensional Groups of Automorphisms},
  author = {Serge Cantat and Hanspeter Kraft and Andriy Regeta and Immanuel van Santen},
  journal= {arXiv preprint arXiv:2605.13510},
  year   = {2026}
}

Comments

11 pages, comments welcome!