Milnor Fiber Boundary of a Non-isolated Surface Singularity

• 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: Mathematics.; Algebraic geometry.; Functions of complex variables.; Algebraic topology.; Several Complex Variables and Analytic Spaces.; Algebraic Geometry.; Algebraic Topology.

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...

Πίνακας περιεχομένων:

• 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.