Foliations on hypersurfaces in holomorphic symplectic manifolds

Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restriction $\sigma|_Y$ of the holomorphic symplectic form induces a rank one foliation on Y. We investigate situations where this foliation has compact leaves; in such cases we obtain a space of leaves Y/F which has dimension 2n-2 and admits a holomorphic symplectic form.