# 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 fo-liations 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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Cited literature [11 references]

https://hal.archives-ouvertes.fr/hal-01671053
Contributor : Frank Loray <>
Submitted on : Thursday, December 21, 2017 - 5:56:21 PM
Last modification on : Monday, February 25, 2019 - 5:16:03 PM

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deg3v1.pdf
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### Identifiers

• HAL Id : hal-01671053, version 1
• ARXIV : 1712.08330

### Citation

Frank Loray, Jorge Pereira, Frédéric Touzet. Deformation of Rational Curves Along Foliations. 2017. ⟨hal-01671053v1⟩

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