Sernesi Deformations of Algebraic Schemes

1. Auflage 2007
ISBN: 978-3-540-30615-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 342 Seiten

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.

Edoardo Sernesi - vita Present 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 Università di Roma ``La Sapienza', 1980-1983.
- Professore ordinario di Geometria Università di Roma ``La Sapienza', 1983-1992.
- Professore ordinario di Geometria Università Roma Tre, from 1992.

Autoren/Hrsg.

Sernesi, Edoardo

Inhaltsverzeichnis

1;Preface;5
2;Contents;8
3;Terminology and notation;11
4;Introduction;13
5;1 Infinitesimal deformations;19
5.1;1.1 Extensions;19
5.2;1.2 Locally trivial deformations;30
6;2 Formal deformation theory;47
6.1;2.1 Obstructions;47
6.2;2.2 Functors of Artin rings;54
6.3;2.3 The theorem of Schlessinger;64
6.4;2.4 The local moduli functors;74
6.5;2.5 Formal versus algebraic deformations;85
6.6;2.6 Automorphisms and prorepresentability;99
7;3 Examples of deformation functors;113
7.1;3.1 Affine schemes;113
7.2;3.2 Closed subschemes;132
7.3;3.3 Invertible sheaves;147
7.4;3.4 Morphisms;166
8;4 The Hilbert schemes and the Quot schemes;197
8.1;4.1 Castelnuovo-Mumford regularity;197
8.2;4.2 Flatness in the projective case;204
8.3;4.3 Hilbert schemes;216
8.4;4.4 Quot schemes;229
8.5;4.5 Flag Hilbert schemes;237
8.6;4.6 Examples and applications;245
8.7;4.7 Plane curves;264
9;A Flatness;279
10;B Differentials;289
11;C Smoothness;303
12;D Complete intersections;315
12.1;D.1 Regular embeddings;315
12.2;D.2 Relative complete intersection morphisms;317
13;E Functorial language;323
14;References;331
15;List of Symbols;339
16;Index;343