Flat webs and homogeneous foliations on the complex projective plane

Par Samir Bedrouni, David Marín

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


© Société Mathématique de France. The aim of this work is to study the foliations on the complex projective plane with flat Legendre transform (dual web). We establish some effective criteria for the flatness of the dual d-web of a homogeneous foliation of degree d and we describe some explicit examples. These results allow us to show that up to automorphism of P2 C there are 11 homogeneous foliations of degree 3 with flat dual web. We will see also that it is possible, under certain assumptions, to bring the study of flatness of the dual web of a general foliation to the homogeneous framework. We get some classification results about foliations with non-degenerate singularities and flat Legendre transform.
Original languageEnglish
Pages (from-to)479-516
JournalBulletin de la Societe Mathematique de France
Issue number3
Publication statusPublished - 1 Jan 2018

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