Milnor Fiber Boundary of a Nonisolated Surface Singularity

Milnor Fiber Boundary of a Non-isolated Surface Singularity (Lecture Notes in Mathematics) by András Némethi and Ágnes Szilárd
English | 2012 | ISBN: 3642236464 | PDF | 240 pages | 2,6 MB

In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber off as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an I.C.I.S. . Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the I.C.I.S. (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.



Title: Milnor Fiber Boundary of a Nonisolated Surface Singularity
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