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Birational geometry of foliations associated to simple derivations

2017/01/03 by Gaël Cousin, Cousin, Gael, Luís Gustavo Mendes +3
Mathematics · #13N15 #14E07 #37F75 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1701.00790

openalex publication_date 2017/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor singularities in the complement of a line. We establish the position of these foliations in the birational classification of foliations and prove the finiteness of their birational symmetries. Most of the results apply to wider classes of foliations.

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