Zariski Hyperplane Section Theorem for Grassmannian Varieties

Let phi : X to M be a morphism from a smooth irreducible complex quasi-projective variety X to a Grassmannian variety M such that the image is of dimension > 2. Let D be a reduced hypersurface in M, and gamma a general linear automorphism of M. We show that, under a certain differential-geometric condition on phi(X) and D, the fundamental group pi1 ( (gamma circ phi)-1 (M\D)) is isomorphic to a central extension of pi1 (M\D) * pi1 (X) by the cokernel of pi2 (phi) :pi2 (X) to pi2 (M).