Vector fields and foliations associated to groups of projective automorphisms

Fabio H. Santos; Bruno Scardua

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arXiv · 0709.0546

Vector fields and foliations associated to groups of projective automorphisms

Fabio H. Santos·Bruno Scardua

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Abstract

We introduce and give normal forms for (one-dimensional) Riccati foliations (vector fields) on $\ov \bc \times \bc P(2)$ and $\ov \bc \times \ov \bc^n$. These are foliations are characterized by transversality with the generic fiber of the first projection and we prove they are conjugate {\em in some invariant Zariski open subset} to the suspension of a group of automorphisms of the fiber, $\bc P(2)$ or $\ov \bc^n$, this group called {\it global holonomy}. Our main result states that given a finitely generated subgroup $G$ of $\Aut(\bc P (2))$, there is a Riccati foliation on $\ov \bc \times \bc P(2)$ for which the global holonomy is conjugate to $G$.

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BibTeX RIS

Fabio H. Santos, Bruno Scardua. 2007-09-04. Vector fields and foliations associated to groups of projective automorphisms. https://arxiv.org/abs/0709.0546

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