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Feuilletages et actions de groupes sur les espaces projectifs

Julie Deserti·Dominique Cerveau
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Abstract

A holomorphic foliation $\mathscr{F}$ on a compact complex manifold $M$ is said to be an $\mathscr{L}$-foliation if there exists an action of a complex Lie group $G$ such that the generic leaf of $\mathscr{F}$ coincides with the generic orbit of $G$. We study $\mathscr{L}$-foliations of codimension one, in particular in projective space, in the spirit of classical invariant theory, but here the invariants are sometimes transcendantal ones. We give a bestiary of examples and general properties. Some classification results are obtained in low dimensions.

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Julie Deserti, Dominique Cerveau. 2004-12-03. Feuilletages et actions de groupes sur les espaces projectifs. https://arxiv.org/abs/math/0412066

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