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Pré-Publication, Document De Travail Année : 2023

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

Résumé

In this work we classify foliations on $\mathbb{CP}^3$ of codimension 1 and degree $2$ 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 $\mathbb{CP}^3$ of codimension 1 and degree $s \geq 3$ that have a line as singular set and such that they form a family with a rational first integral of degree $s+1$ or they are logarithmic foliations where some of them have a minimal rational first integral of degree not bounded.

Dates et versions

hal-03919766 , version 1 (03-01-2023)

Identifiants

Citer

Claudia R. Alcántara, Dominique Cerveau. Foliations on $\mathbb{CP}^3$ of degree $2$ that have a line as singular set. 2023. ⟨hal-03919766⟩
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