English

On holomorphic $\mathbb{C}^*$-actions

Complex Variables 2024-08-26 v2

Abstract

In this paper we study holomorphic actions of the complex multiplicative group on complex manifolds around a singular (fixed) point. We prove linearization results for the germ of action and also for the whole action under some conditions on the manifold. This can be seen as a follow-up to previous works of M. Suzuki and other authors.

Keywords

Cite

@article{arxiv.2408.09625,
  title  = {On holomorphic $\mathbb{C}^*$-actions},
  author = {Víctor León and Bruno Scárdua},
  journal= {arXiv preprint arXiv:2408.09625},
  year   = {2024}
}
R2 v1 2026-06-28T18:16:10.794Z