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 of codimension 1 and degree 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 of codimension 1 and degree that have a line as singular set and such that they form a family with a rational first integral of degree 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