The boundary of the Milnor fiber for some non-isolated germs of complex surfaces

Details The boundary of the Milnor fiber for some non-isolated germs of complex surfaces The boundary of the Milnor fiber for some non-isolated germs of complex surfaces

2006-05-04

arxiv.org/abs/math/0605123v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

We study the boundary L_t of the Milnor fiber for the non-isolated singularities in C^3 with equation z^m - g(x,y) = 0 where g(x,y) is a non-reduced plane curve germ. We give a complete proof that L_t is a Waldhausen graph manifold and we provide the tools to construct its plumbing graph. As an example, we give the plumbing graph associated to the germs z^2 - (x^2 - y^3)y^l = 0 with l an interger >1. We prove that the boundary of the Milnor fiber is a Waldhausen manifold new in complex geometry, as it cannot be the boundary of a normal surface singularity.

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