SEMI-SIMPLE CARROUSELS AND THE MONODROMY

Abstract. Let U be an open neighborhood of the origin in Cn+1 and let f: (U,0) → (C, 0) be complex analytic. Let z0 be a generic linear form on Cn+1. If the relative polar curve Γ1f,z0 at the origin is irreducible and the intersection number Γ1f,z0 · V (f))0 is prime, then there are severe restrictions on the possible degree n cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when Γ1f,z0 · V (f))0 is not prime