English

Codimension two torus actions on the affine space

Algebraic Geometry 2024-11-25 v1

Abstract

In this paper, we classify smooth, contractible affine varieties equipped with faithful torus actions of complexity two, having a unique fixed point and a two-dimensional algebraic quotient isomorphic to a toric blow-up of a toric surface. These varieties are of particular interest as they represent the simplest candidates for potential counterexamples to the linearization conjecture in affine geometry.

Keywords

Cite

@article{arxiv.2411.14645,
  title  = {Codimension two torus actions on the affine space},
  author = {Alvaro Liendo and Charlie Petitjean},
  journal= {arXiv preprint arXiv:2411.14645},
  year   = {2024}
}

Comments

11 pages

R2 v1 2026-06-28T20:08:33.964Z