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Journal Articles Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Year : 2020

Deformation of Rational Curves Along Foliations

Abstract

Deformation of morphisms along leaves of foliations define the tangential foliation on the corresponding space of morphisms. We prove that codimension one foliations having a tangential foliation with at least one non-algebraic leaf are transversely homogeneous with structure group determined by the codimension of the non-algebraic leaf in its Zariski closure. As an application, we provide a structure theorem for degree three foliations on $P^3$ .
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Dates and versions

hal-01671053 , version 1 (21-12-2017)
hal-01671053 , version 2 (29-08-2018)

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Frank Loray, Jorge Vitório Pereira, Frédéric Touzet. Deformation of Rational Curves Along Foliations. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2020, 21 (Special issue), pp.1315-1331. ⟨hal-01671053v2⟩
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