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Semi-simple Carrousels and the Monodromy

David B. Massey (2006)

Annales de l’institut Fourier

Let 𝒰 be an open neighborhood of the origin in n + 1 and let f : ( 𝒰 , 0 ) ( , 0 ) be complex analytic. Let z 0 be a generic linear form on n + 1 . If the relative polar curve Γ f , z 0 1 at the origin is irreducible and the intersection number ( Γ f , z 0 1 · 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 ( Γ f , z 0 1 · V ( f ) ) 0 is not prime.

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