Milnor fiber boundary of a nonisolated surface singularity
 Author/Creator
 Némethi, András.
 Language
 English.
 Imprint
 Berlin ; New York : Springer, c2012.
 Physical description
 xii, 240 p. : ill. ; 24 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2037.
Access
Available online

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QA3 .L28 V.2037

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QA3 .L28 V.2037
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Contributors
 Contributor
 Szilárd, Ágnes.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 231236) and index.
 Contents

 1 Introduction. 2 The topology of a hypersurface germ f in three variables Milnor fiber. 3 The topology of a pair (f g). 4 Plumbing graphs and oriented plumbed 3manifolds. 5 Cyclic coverings of graphs. 6 The graph GC of a pair (f g). The definition. 7 The graph GC . Properties. 8 Examples. Homogeneous singularities. 9 Examples. Families associated with plane curve singularities. 10 The Main Algorithm. 11 Proof of the Main Algorithm. 12 The Collapsing Main Algorithm. 13 Vertical/horizontal monodromies. 14 The algebraic monodromy of H1(u F). Starting point. 15 The ranks of H1(u F) and H1(u F nVg) via plumbing. 16 The characteristic polynomial of u F via P# and P#. 18 The mixed Hodge structure of H1(u F). 19 Homogeneous singularities. 20 Cylinders of plane curve singularities: f = f 0(xy). 21 Germs f of type z f 0(xy). 22 The T[currency][currency][currency]family. 23 Germs f of type f (xayb z). Suspensions. 24 Peculiar structures on u F. Topics for future research. 25 List of examples. 26 List of notations.
 (source: Nielsen Book Data)
 Publisher's Summary
 In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging nonisolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3manifold. 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 András Némethi, Ágnes Szilárd.
 Series
 Lecture notes in mathematics ; 2037
 ISBN
 9783642236464
 3642236464
 9783642236471 (ebook)
 3642236472 (ebook)
 Publisher Number
 Best.Nr.: 80112041