Feuilletages et transformations p\'eriodiques
Dominique Cerveau, Julie D\'eserti

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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Mathematics and Applications
