Abstract
Let F be a codimension one holomorphic singular foliation on M n . F is transversely affine respectively transversely projective if so it is its regular foliation. We consider foliations which are transversely affine or projective in MΛ for some analytic codimension one invariant subset λ ⊂ M. Examples are logarithmic and Riccati foliations on CP(2). In the projective case ther is a dual foliation F ⊥ generically transverse to F . F ⊥ is a fibration if F is Riccati. We prove: 1. Let F be given on CP(2), transversely affine outside an algebraic invariant curve Λ. Suppose that F has reduced non-degenerate singularities in Λ. Then F is logarithmic. 2. Let F be given on CP( n ), transversely projective non-affine, outside an invariant algebraic hypersurface Λ. Then F ⊥ extends to CP( n ). If this extension has a meromorphic first integral, then F is Riccati rational pull-back.
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