Milnor Fiber Boundary of a Non-isolated Surface Singularity (Lecture Notes in Mathematics)

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9783642236464: Milnor Fiber Boundary of a Non-isolated Surface Singularity (Lecture Notes in Mathematics)
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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 off 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 I.C.I.S. . Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the I.C.I.S. (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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“The aim of this book is to study the topological types of the oriented smooth 3-manifolds appearing as boundaries ∂F of the Milnor fibers of complex surface singularities of embedding dimension 3, as well as the monodromy actions on their homology. ... It is clearly invaluable for anybody interested in the topology of non-isolated complex surface singularities and even of singularities of real analytic spaces of dimension 4.” (Patrick Popescu-Pampu, Mathematical Reviews, January, 2014)

“The book describes three manifolds which occur in relation with complex hypersurfaces in C3 near singular points. ... I recommend it to all students and researchers who are interested in the local topology of algebraic varieties. It contains a good description of techniques, such as plumbing, cyclic coverings, monodromy, et cetera. The book is well written and ends with several topics for future research.” (Dirk Siersma, Nieuw Archief voor Wiskunde, Vol. 14 (2), June, 2013)

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Book Description Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Germany, 2012. Paperback. Condition: New. 2012. Language: English. Brand new Book. 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. Seller Inventory # LIB9783642236464

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Book Description Springer-Verlag Gmbh Jan 2012, 2012. Taschenbuch. Condition: Neu. Neuware - 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. 240 pp. Englisch. Seller Inventory # 9783642236464

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