000			03798nam a22005055i 4500
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
024	7		_a10.1007/978-3-642-23647-1 _2doi
050		4	_aQA331.7
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.94 _223
100	1		_aNémethi, András. _eauthor.
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.
300			_aXII, 240p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
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