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008			150903s2007 gw | o |||| 0|eng d
020			_a9783540284192 _99783540284192
024	7		_a10.1007/3540284192 _2doi
035			_avtls000347149
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040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA564-609
100	1		_aGreuel, Gert-Martin. _eautor _9327571
245	1	0	_aIntroduction to Singularities and Deformations / _cby Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2007.
300			_axii, 472 páginas 54 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aSpringer Monographs in Mathematics, _x1439-7382
500			_aSpringer eBooks
505	0		_aI. Singularity Theory. Basic Properties of Complex Spaces and Germs. Weierstrass Preparation and Finiteness Theorem. Application to Analytic Algebras. Complex Spaces. Complex Space Germs and Singularities. Finite Morphisms and Finite Coherence Theorem. Applications of the Finite Coherence Theorem. Finite Morphisms and Flatness. Flat Morphisms and Fibres. Singular Locus and Differential Forms. Hypersurface Singularities. Invariants of Hypersurface Singularities. Finite Determinacy. Algebraic Group Actions. Classification of Simple Singularities. Plane Curve Singularities. Parametrization. Intersection Multiplicity. Resolution of Plane Curve Singularities. Classical Topological and Analytic Invariants -- II. Local Deformation Theory. Deformations of Complex Space Germs. Deformations of Singularities. Embedded Deformations. Versal Deformations. Infinitesimal Deformations. Obstructions. Equisingular Deformations of Plane Curve Singularities -- Equisingular Deformations of the Equation. The Equisingularity Ideal. Deformations of the Parametrization. Computation of T^1 and T^2 . Equisingular Deformations of the Parametrization. Equinormalizable Deformations. Versal Equisingular Deformations -- Appendices: Sheaves. Commutative Algebra. Formal Deformation Theory. Literature -- Index.
520			_aSingularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. Plane curve singularities are a classical object of study, rich of ideas and applications, which still is in the center of current research and as such provides an ideal introduction to the general theory. Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete. In the first part of the book the authors develop the relevant techniques, including the Weierstraß preparation theorem, the finite coherence theorem etc., and then treat isolated hypersurface singularities, notably the finite determinacy, classification of simple singularities and topological and analytic invariants. In local deformation theory, emphasis is laid on the issues of versality, obstructions, and equisingular deformations. The book moreover contains a new treatment of equisingular deformations of plane curve singularities including a proof for the smoothness of the mu-constant stratum which is based on deformations of the parameterization. Computational aspects of the theory are discussed as well. Three appendices, including basic facts from sheaf theory, commutative algebra, and formal deformation theory, make the reading self-contained. The material, which can be found partly in other books and partly in research articles, is presented from a unified point of view for the first time. It is given with complete proofs, new in many cases. The book thus can serve as source for special courses in singularity theory and local algebraic and analytic geometry.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700	1		_aLossen, Christoph. _eautor _9327572
700	1		_aShustin, Eugenii. _eautor _9325129
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9783540283805
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/3-540-28419-2 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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