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 |
Table des matières:
- 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.
- 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