TRANSVERSELY AFFINE AND TRANSVERSELY PROJECTIVE HOLOMORPHIC FOLIATIONS

Let F be a codimension one holomorphic singular foliation on M(n). F i s transversely affine respectively transversely projective if so it is its regular foliation. We consider foliations which are transversely affine or projective in M\Lambda for some analytic codimension one inv ariant subset Lambda subset of M. Examples are logarithmic and Riccati foliations on CP(2). In the projective case ther is a dual foliation F-perpendicular to generically transverse to F. F-perpendicular to is a fibration if F is Riccati. We prove: 1. Let F be given on CP(2), tra nsversely affine outside an algebraic invariant curve Lambda. Suppose that F has reduced non-degenerate singularities in Lambda. Then F is l ogarithmic. 2. Let F be given on CP(n), transversely projective non-af fine, outside an invariant algebraic hypersurface Lambda. Then F(perpe ndicular to)extends to CP(n). If this extension has a meromorphic firs t integral, then F is Riccati rational pull-back.