Milnor Fiber Boundary of a Non-Isolated Surface Singularity

By Andr?'s N. Methi, Gnes Szil Rd, Agnes Szilard, et al.

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 of f 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 ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (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.

• Format: Paperback
• Language: English
• ISBN: 3642236464
• ISBN13: 9783642236464
• Release Date: January 2012
• Publisher: Springer
• Length: 240 Pages
• Weight: 0.80 lbs.
• Dimensions: 0.7" x 6.0" x 9.0"