English

Global dynamics and perspectives on singularities of holomorphic foliations

Dynamical Systems 2023-01-16 v1 Classical Analysis and ODEs Complex Variables

Abstract

In dimensions greater than or equal to 3, the local structure of a singular holomorphic foliation conceals a globally defined foliation on the projective space of dimension one less. In this paper, we will discuss how the global dynamics of the latter foliation exerts influence on several problems that apparently have a purely local nature. In the course of the discussion, a few recent results and open problems in the area will be reviewed as well.

Keywords

Cite

@article{arxiv.2301.05534,
  title  = {Global dynamics and perspectives on singularities of holomorphic foliations},
  author = {Julio C. Rebelo and Helena Reis},
  journal= {arXiv preprint arXiv:2301.05534},
  year   = {2023}
}