Deformations of Algebraic Schemes
(Sprache: Englisch)
This account of deformation theory in classical algebraic geometry over an algebraically closed field presents for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet relevant to algebraic...
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This account of deformation theory in classical algebraic geometry over an algebraically closed field presents for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet relevant to algebraic geometers. 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.
Inhaltsverzeichnis zu „Deformations of Algebraic Schemes “
- 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
Autoren-Porträt von Edoardo Sernesi
Edoardo Sernesi - vitaPresent position: Professore ordinario di Geometria, Facoltà di Scienze MFN, Università Roma Tre
Education:
- Laurea in Matematica - Università di Roma, 1969
- Ph.D. in Mathematics - Brandeis University, 1976
Professional experience:
- Assistente ordinario di Geometria, Università di Ferrara, 1974-1980.
- Professore straordinario di Geometria Universitàdi Roma "La Sapienza", 1980-1983.
- Professore ordinario di Geometria Universitàdi Roma "La Sapienza", 1983-1992.
- Professore ordinario di Geometria Università Roma Tre, from 1992.
Bibliographische Angaben
- Autor: Edoardo Sernesi
- 2006, 2006, 342 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540306080
- ISBN-13: 9783540306085
- Erscheinungsdatum: 06.07.2006
Sprache:
Englisch
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