000 | 03798nam a22005055i 4500 | ||
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001 | 978-3-642-23647-1 | ||
003 | DE-He213 | ||
005 | 20140220083302.0 | ||
007 | cr nn 008mamaa | ||
008 | 120104s2012 gw | s |||| 0|eng d | ||
020 |
_a9783642236471 _9978-3-642-23647-1 |
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024 | 7 |
_a10.1007/978-3-642-23647-1 _2doi |
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050 | 4 | _aQA331.7 | |
072 | 7 |
_aPBKD _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
|
082 | 0 | 4 |
_a515.94 _223 |
100 | 1 |
_aNémethi, András. _eauthor. |
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245 | 1 | 0 |
_aMilnor Fiber Boundary of a Non-isolated Surface Singularity _h[electronic resource] / _cby András Némethi, Ágnes Szilárd. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012. |
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300 |
_aXII, 240p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2037 |
|
505 | 0 | _a1 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 | _aIn 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 | _aMathematics. | |
650 | 0 | _aGeometry, algebraic. | |
650 | 0 | _aDifferential equations, partial. | |
650 | 0 | _aAlgebraic topology. | |
650 | 1 | 4 | _aMathematics. |
650 | 2 | 4 | _aSeveral Complex Variables and Analytic Spaces. |
650 | 2 | 4 | _aAlgebraic Geometry. |
650 | 2 | 4 | _aAlgebraic Topology. |
700 | 1 |
_aSzilárd, Ágnes. _eauthor. |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783642236464 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2037 |
|
856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-642-23647-1 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c102205 _d102205 |