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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Némethi, András (Συγγραφέας), Szilárd, Ágnes (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
Σειρά:Lecture Notes in Mathematics, 2037
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Némethi, András.  |e author. 
245 1 0 |a Milnor Fiber Boundary of a Non-isolated Surface Singularity  |h [electronic resource] /  |c by András Némethi, Ágnes Szilárd. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg,  |c 2012. 
300 |a XII, 240 p.  |b online resource. 
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490 1 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 2037 
505 0 |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. 
520 |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. 
650 0 |a Mathematics. 
650 0 |a Algebraic geometry. 
650 0 |a Functions of complex variables. 
650 0 |a Algebraic topology. 
650 1 4 |a Mathematics. 
650 2 4 |a Several Complex Variables and Analytic Spaces. 
650 2 4 |a Algebraic Geometry. 
650 2 4 |a Algebraic Topology. 
700 1 |a Szilárd, Ágnes.  |e author. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783642236464 
830 0 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 2037 
856 4 0 |u http://dx.doi.org/10.1007/978-3-642-23647-1  |z Full Text via HEAL-Link 
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950 |a Mathematics and Statistics (Springer-11649)