Deformations of algebraic schemes
The study of small and local deformations of algebraic varieties originates in the classical work of Kodaira and Spencer and its formalization by Grothendieck in the late 1950's. It has become increasingly important in algebraic geometry in every context where variational phenomena come into pl...
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2006. |
| Collection: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
334 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Description d'après consultation du 17 mars 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Deformations of Algebraic Schemes, Texte imprimé, 9783540818229 • Deformations of Algebraic Schemes, Texte imprimé, 9783642067877 • Deformations of algebraic schemes, Edoardo Sernesi, 2006, Berlin, Springer, 1 vol. (XI-339 p.), Grundlehren der mathematischen Wissenschaften, 978-3-540-30608-5 |
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| 100 | 1 | |a Sernesi, Edoardo, |d 1947- | |
| 245 | 1 | 0 | |a Deformations of algebraic schemes |c Edoardo Sernesi. |
| 250 | |a 1st ed. 2006. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |v 334 |x 2196-9701 | |
| 500 | |a Description d'après consultation du 17 mars 2011 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. [321]-328. Index | ||
| 505 | 1 | |a Introduction Infinitesimal Deformations: Extensions. Locally Trivial Deformations Formal Deformation Theory: Obstructions. Extensions of Schemes. Functors of Artin Rings. The Theorem of Schlessinger. The Local Moduli Functors Formal Versus Algebraic Deformations. Automorphisms and Prorepresentability Examples of Deformation Functors: Affine Schemes. Closed Subschemes. Invertible Sheaves. Morphisms Hilbert and Quot Schemes: Castelnuovo-Mumford Regularity. Flatness in the Projective Case. Hilbert Schemes. Quot Schemes. Flag Hilbert Schemes. Examples and Applications. Plane Curves Appendices: Flatness. Differentials. Smoothness. Complete Intersections. Functorial Language List of Symbols Bibliography. | |
| 505 | 0 | |a Introduction -- Infinitesimal Deformations: Extensions. Locally Trivial Deformations -- Formal Deformation Theory: Obstructions. Extensions of Schemes. Functors of Artin Rings. The Theorem of Schlessinger. The Local Moduli Functors -- Formal Versus Algebraic Deformations. Automorphisms and Prorepresentability -- Examples of Deformation Functors: Affine Schemes. Closed Subschemes. Invertible Sheaves. Morphisms -- Hilbert and Quot Schemes: Castelnuovo-Mumford Regularity. Flatness in the Projective Case. Hilbert Schemes. Quot Schemes. Flag Hilbert Schemes. Examples and Applications. Plane Curves -- Appendices: Flatness. Differentials. Smoothness. Complete Intersections. Functorial Language -- List of Symbols -- Bibliography | |
| 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 The study of small and local deformations of algebraic varieties originates in the classical work of Kodaira and Spencer and its formalization by Grothendieck in the late 1950's. It has become increasingly important in algebraic geometry in every context where variational phenomena come into play, and in classification theory, e.g. the study of the local properties of moduli spaces.Today deformation theory is highly formalized and has ramified widely within mathematics. This self-contained account of deformation theory in classical algebraic geometry (over an algebraically closed field) brings together for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet of everyday relevance to algebraic geometers. Based on Grothendieck's functorial approach it covers formal deformation theory, algebraization, isotriviality, Hilbert schemes, Quot schemes and flag Hilbert schemes. It includes applications to the construction and properties of Severi varieties of families of plane nodal curves, space curves, deformations of quotient singularities, Hilbert schemes of points, local Picard functors, etc. Many examples are provided. Most of the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry | ||
| 650 | |a Schémas (géométrie algébrique) | ||
| 776 | 0 | |t Deformations of Algebraic Schemes |b Texte imprimé |z 9783540818229 | |
| 776 | 0 | |t Deformations of Algebraic Schemes |b Texte imprimé |z 9783642067877 | |
| 776 | 0 | |0 112121314 |t Deformations of algebraic schemes |f Edoardo Sernesi |d 2006 |c Berlin |n Springer |p 1 vol. (XI-339 p.) |s Grundlehren der mathematischen Wissenschaften |z 978-3-540-30608-5 | |
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| 997 | |0 938421 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||