  Let $\Cal U$ be an open neighborhood of the origin in $\Bbb C^{n+1}$ and let
$f:(\Cal U, \bold 0)\to(\Bbb C, 0)$ be complex analytic. Let $z_0$ be a generic
linear form on $\Bbb C^{n+1}$. If the relative polar curve $\Gamma^1_{f, z_0}$
at the origin is irreducible and the intersection number $\big(\Gamma^1_{f,
z_0}\cdot V(f))_\bold 0$ 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 $\big(\Gamma^1_{f, z_0}\cdot
V(f))_\bold 0$ is not prime.
