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Milnor Fiber Boundary of a Non-isolated Surface Singularity / by András Némethi, Ágnes Szilárd
(Lecture Notes in Mathematics. ISSN:16179692 ; 2037)
版 | 1st ed. 2012. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2012 |
本文言語 | 英語 |
大きさ | XII, 240 p : online resource |
著者標目 | *Némethi, András author Szilárd, Ágnes author SpringerLink (Online service) |
件 名 | LCSH:Functions of complex variables LCSH:Algebraic geometry LCSH:Algebraic topology FREE:Several Complex Variables and Analytic Spaces FREE:Algebraic Geometry FREE:Algebraic Topology |
一般注記 | 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 -- 12The 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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-23647-1 |
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Springer eBooks | 9783642236471 |
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EB00236082 |
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