Semi-simple Carrousels and the Monodromy

Details Semi-simple Carrousels and the Monodromy Semi-simple Carrousels and the Monodromy

2004-10-06

arxiv.org/abs/math/0410189v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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.

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