The boundary of the Milnor fibre of complex and real analytic non-isolated singularities

Details The boundary of the Milnor fibre of complex and real analytic non-isolated singularities The boundary of the Milnor fibre of complex and real analytic non-isolated singularities

2011-06-24

arxiv.org/abs/1106.4956v1

Mathematics

Algebraic Geometry

Scientific paper

Let f and g be holomorphic functions vanishing at the origin of the affine space of dimension three. Suppose that the singular set of the zero set of the product fg is 1-dimensional and that the real analytic function $f\bar g$ has an isolated critical value at 0. By results of A. Pichon and J. Seade the function $f\bar g$ has a Milnor fibration. We prove that the boundary of the Milnor fibre is a Waldhausen manifold. As a intermediate milestone we describe geometrically the Milnor fibre of functions of type $f\bar g$ defined in the complex plane, and prove an A'Campo-type formula for the zeta function of their monodromy.

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