English

Foliations on $\mathbb{CP}^3$ of degree $2$ that have a line as singular set

Algebraic Geometry 2022-12-21 v1

Abstract

In this work we classify foliations on CP3\mathbb{CP}^3 of codimension 1 and degree 22 that have a line as singular set. To achieve this, we do a complete description of the components. We prove that the boundary of the exceptional component has only 3 foliations up to change of coordinates, and this boundary is contained in a logarithmic component. Finally we construct examples of foliations on CP3\mathbb{CP}^3 of codimension 1 and degree s3s \geq 3 that have a line as singular set and such that they form a family with a rational first integral of degree s+1s+1 or they are logarithmic foliations where some of them have a minimal rational first integral of degree not bounded.

Keywords

Cite

@article{arxiv.2212.09845,
  title  = {Foliations on $\mathbb{CP}^3$ of degree $2$ that have a line as singular set},
  author = {Claudia R. Alcántara and Dominique Cerveau},
  journal= {arXiv preprint arXiv:2212.09845},
  year   = {2022}
}

Comments

14 pages. Comments are welcome