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Milnor Fiber Boundary of a Non-isolated Surface Singularity
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 a...
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| Auteurs principaux : | , |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Milnor Fiber Boundary of a Non-isolated Surface Singularity / András Némethi, Ágnes Szilárd. |
| Édition : | 1st ed. 2012. |
| Publié : |
Berlin, Heidelberg :
Springer Berlin Heidelberg
, [20..] Cham : Springer Nature |
| Collection : | Lecture notes in mathematics (Internet) ; 2037 |
| Accès en ligne : |
Accès Nantes Université
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| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | 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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| Documents associés : | Autre format:
Milnor fiber boundary of a non-isolated surface singularity Autre format: Milnor Fiber Boundary of a Non-isolated Surface Singularity Autre format: Milnor fiber boundary of a non-isolated surface singularity |
| Résumé : | 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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| Notes : | L'impression du document génère 236 p. |
| Bibliographie : | Bibliogr. Index |
| ISBN : | 978-3-642-23647-1 |
| DOI : | 10.1007/978-3-642-23647-1 |