Submanifolds with ample normal bundle

We construct germs of complex manifolds of dimension m along projective submanifolds of dimension n$n$ with ample normal bundle and without nonconstant meromorphic functions whenever m >= 2n. We also show that our methods do not allow the construction of similar examples when m >= 2n by establishing an algebraicity criterion for foliations on projective spaces that generalizes a classical result by Van den Ven characterizing linear subspaces of projective spaces as the only submanifolds with split tangent sequence.