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|a 9783642236471
|9 978-3-642-23647-1
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|a 10.1007/978-3-642-23647-1
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|a QA331.7
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|a MAT034000
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|a 515.94
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|a Némethi, András.
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|a Milnor Fiber Boundary of a Non-isolated Surface Singularity
|h [electronic resource] /
|c by András Némethi, Ágnes Szilárd.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg,
|c 2012.
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|a XII, 240 p.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 2037
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|a 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 3-manifolds -- 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(¶ F). Starting point -- 15 The ranks of H1(¶ F) and H1(¶ F nVg) via plumbing -- 16 The characteristic polynomial of ¶ F via P# and P# -- 18 The mixed Hodge structure of H1(¶ F) -- 19 Homogeneous singularities -- 20 Cylinders of plane curve singularities: f = f 0(x;y) -- 21 Germs f of type z f 0(x;y) -- 22 The T;;–family -- 23 Germs f of type ˜ f (xayb; z). Suspensions -- 24 Peculiar structures on ¶ F. Topics for future research -- 25 List of examples -- 26 List of notations.
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|a 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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|a Mathematics.
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|a Algebraic geometry.
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|a Functions of complex variables.
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|a Algebraic topology.
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|a Mathematics.
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|a Several Complex Variables and Analytic Spaces.
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|a Algebraic Geometry.
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|a Algebraic Topology.
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|a Szilárd, Ágnes.
|e author.
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783642236464
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 2037
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|u http://dx.doi.org/10.1007/978-3-642-23647-1
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a ZDB-2-LNM
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|a Mathematics and Statistics (Springer-11649)
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