Milnor fiber boundary of a non-isolated surface singularity
- András Némethi, Ágnes Szilárd.
- Berlin ; New York : Springer, c2012.
- Physical description
- xii, 240 p. : ill. ; 24 cm.
- Lecture notes in mathematics (Springer-Verlag) 2037.
Math & Statistics Library
QA3 .L28 V.2037
- Unknown QA3 .L28 V.2037
- Includes bibliographical references (p. 231-236) and index.
- 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(u F). Starting point.- 15 The ranks of H1(u F) and H1(u F nVg) via plumbing.- 16 The characteristic polynomial of u F via P# and P#.- 18 The mixed Hodge structure of H1(u 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[currency]--[currency]--[currency]-family.- 23 Germs f of type f (xayb-- z). Suspensions.- 24 Peculiar structures on u F. Topics for future research.- 25 List of examples.- 26 List of notations.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- Publication date
- Lecture notes in mathematics ; 2037
- 9783642236471 (e-book)
- 3642236472 (e-book)
- Publisher Number
- Best.-Nr.: 80112041