We give the first (as far as we know) complete description of the boundary of the Milnor fiber for some non-isolated singular germs of surfaces in C 3 . We study irreducible (i.e. gcd (m, k, l) = 1) non-isolated (i.e. 1 ≤ k < l) Hirzebruch hypersurface singularities in C 3 given by the equation z m − x k y l = 0. We show that the boundary L of the Milnor fiber is always a Seifert manifold and we give an explicit description of the Seifert structure. From it, we deduce that: 1) L is never diffeomorphic to the boundary of the normalization.2) L is a lens space iff m = 2 and k = 1.3) When L is not a lens space, it is never orientation preserving diffeomorphic to the boundary of a normal surface singularity.
Abstract. We define an equivalence relation, called algebraic cobordism, on the set of bilinear forms over the integers. When n ≥ 3, we prove that two 2n − 1 dimensional, simple fibered links are cobordant if and only if they have algebraically cobordant Seifert forms. As an algebraic link is a simple fibered link, our criterion for cobordism allows us to study isolated singularities of complex hypersurfaces up to cobordism.Mathematics Subject Classification (1991). 57R, 57R80, 57R90, 57M25, 57Q45, 32S, 32S55, 14B05.
We consider a finite analytic morphism φ = (f, g) : (X, p) −→ (C 2 , 0) where (X, p) is a complex analytic normal surface germ and f and g are complex analytic function germs.We denote G(Y ) the dual graph of the resolution π. We study the behaviour of the Hironaka quotients of (f, g) associated to the vertices of G(Y ). We show that there exists maximal oriented arcs in G(Y ) along which the Hironaka quotients of (f, g) strictly increase and they are constant on the connected components of the closure of the complement of the union of the maximal oriented arcs.
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