Milnor fiber boundary of a non-isolated surface singularity / / Andras Nemethi, Agnes Szilard

• Record Nr.: UNINA9910132668203321
• Autore: Nemethi Andras
• Pubbl/distr/stampa: Heidelberg ; ; New York, : Springer, c2012
• ISBN: 9783642236471; 3642236472
• Edizione: [1st ed. 2012.]
• Descrizione fisica: 1 online resource (XII, 240 p.)
• Collana: Lecture notes in mathematics, , 0075-8434 ; ; 2037
• Altri autori (Persone): SzilardAgnes
• Disciplina: 514
• Soggetti: Topology; Milnor fibration; Singularities (Mathematics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references (p. 231-236) and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.