Ebook: 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 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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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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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
Content:
Front Matter....Pages i-xii
Front Matter....Pages 9-9
The Topology of a Hypersurface Germ f in Three Variables....Pages 11-15
The Topology of a Pair (f,g)....Pages 17-23
Plumbing Graphs and Oriented Plumbed 3-Manifolds....Pages 25-43
Cyclic Coverings of Graphs....Pages 45-54
Examples: Homogeneous Singularities....Pages 55-61
Examples: Families Associated with Plane Curve Singularities....Pages 63-77
Front Matter....Pages 79-82
The Main Algorithm....Pages 83-97
Proof of the Main Algorithm....Pages 99-99
The Collapsing Main Algorithm....Pages 101-115
Vertical/Horizontal Monodromies....Pages 117-130
The Proof of the Characteristic Polynomial Formulae....Pages 131-138
Front Matter....Pages 139-151
Homogeneous Singularities....Pages 153-156
Introduction....Pages 157-160
Front Matter....Pages 161-166
Front Matter....Pages 167-172
Peculiar Structures on ?F: Topics for Future Research....Pages 173-176
Back Matter....Pages 177-177
....Pages 179-199