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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 fiberof the first projection and we prove they are conjugate {\em in some invariantZariski open subset} to the suspension of a group of automorphisms of thefiber, $\bc P(2)$ or $\ov \bc^n$, this group called {\it global holonomy}. Ourmain 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 theglobal holonomy is conjugate to $G$.

Vector fields and foliations associated to groups of projective automorphisms