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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Milnor Fiber Boundary of a Non-Isolated Surface Singularity

Milnor Fiber Boundary of a Non-Isolated Surface Singularity

Szilárd, Ágnes
Némethi, András

Paperback

Series: Lecture Notes in Mathematics, Book 2037

General MathematicsGeometry

ISBN10: 3642236464
ISBN13: 9783642236464
Publisher: Springer
Published: Jan 6 2012
Pages: 240
Weight: 0.80
Height: 0.70 Width: 6.00 Depth: 9.00
Language: English
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.

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