Feuilletages et transformations p\'eriodiques

TL;DR

This paper introduces an effective method to explicitly construct birational involutions associated with quadratic foliations on the complex projective plane, extending classical results and exploring new trivolutions for degree 3 foliations.

Contribution

It provides a practical approach to associate birational involutions with quadratic foliations, improving upon Bertini's classical geometric classification.

Findings

Associates birational involutions to quadratic foliations

Constructs Geiser involutions explicitly in generic cases

Obtains trivolutions from certain degree 3 foliations

Abstract

Bertini classified the birational involutions of the complex projective plane, but his geometric approach does not allow to explicit these maps easily. In this article, we present an effective approach to this problem by associating to each quadratic foliation a birational involution which is, in the generic case, a Geiser involution; this subject has already been covered by Geiser, Milinowski, Williams and alt. We end by making experiences, obtaining trivolutions from some foliations of degree 3.