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

2006/05/04 by Michel, Francoise, Pichon, Anne, Weber, Claude
#14J17 #32S25 #57M25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.math/0605123

Abstract

We study the boundary L_t of the Milnor fiber for the non-isolated singularities in C³ 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 z² - (x² - y³)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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