Introduction to Singularities and Deformations
Singularity 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 t...
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| Główni autorzy: | , , |
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| Format: | Livre numérique |
| Język: | Anglais |
| Wydane: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Wydanie: | 1st ed. 2007. |
| Seria: | Springer Monographs in Mathematics
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| Hasła przedmiotowe: | |
| Dostęp online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Komentarz: |
L'impression du document génère 484 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Introduction to singularities and deformations, G.-M. Greuel, C. Lossen, E. Shustin, 2007, Berlin, Springer, 1 volume (XII-471 pages), Springer monographs in mathematics, 978-3-540-28380-5 • Introduction to Singularities and Deformations, Texte imprimé, 9783540814498 |
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| 020 | |a 9783540284192 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512 | ||
| 084 | |a 14B05. 2010 | ||
| 084 | |a 14B07. 2010 | ||
| 084 | |a 14Hxx. 2010 | ||
| 084 | |a 32S10. 2010 | ||
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| 084 | |a 32S45. 2010 | ||
| 100 | 1 | |a Greuel, Gert-Martin, |d 1944- | |
| 245 | 1 | 0 | |a Introduction to Singularities and Deformations |c G-M. Greuel, C. Lossen, E. Shustin. |
| 250 | |a 1st ed. 2007. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Monographs in Mathematics |x 2196-9922 | |
| 500 | |a L'impression du document génère 484 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a I. 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a Singularity 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 | ||
| 650 | |a Géométrie algébrique | ||
| 650 | |a Singularités (mathématiques) | ||
| 650 | |a Géométrie analytique | ||
| 700 | 1 | |a Lossen, Christoph, |d 19..- |4 aut | |
| 700 | 1 | |a Shustin, Eugenii I., |d 1957- |4 aut | |
| 776 | 0 | |0 113583699 |t Introduction to singularities and deformations |f G.-M. Greuel, C. Lossen, E. Shustin |d 2007 |c Berlin |n Springer |p 1 volume (XII-471 pages) |s Springer monographs in mathematics |z 978-3-540-28380-5 | |
| 776 | 0 | |t Introduction to Singularities and Deformations |b Texte imprimé |z 9783540814498 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/3-540-28419-2 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-R4BHKJZK-1 |z Accès sur la plateforme Istex | |
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| 856 | 4 | |5 180339901:750899530 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/3-540-28419-2 |z Accès INSA CVL | |
| 997 | |0 939041 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||