Deformations of Algebraic Schemes

Cover
Springer Science & Business Media, 20.04.2007 - 342 Seiten
0 Rezensionen
Rezensionen werden nicht überprüft, Google sucht jedoch gezielt nach gefälschten Inhalten und entfernt diese
In one sense, deformation theory is as old as algebraic geometry itself: this is because all algebro-geometric objects can be “deformed” by suitably varying the coef?cients of their de?ning equations, and this has of course always been known by the classical geometers. Nevertheless, a correct understanding of what “deforming” means leads into the technically most dif?cult parts of our discipline. It is fair to say that such technical obstacles have had a vast impact on the crisis of the classical language and on the development of the modern one, based on the theory of schemes and on cohomological methods. The modern point of view originates from the seminal work of Kodaira and Spencer on small deformations of complex analytic manifolds and from its for- lization and translation into the language of schemes given by Grothendieck. I will not recount the history of the subject here since good surveys already exist (e. g. [27], [138], [145], [168]). Today, while this area is rapidly developing, a self-contained text covering the basic results of what we can call “classical deformation theory” seems to be missing. Moreover, a number of technicalities and “well-known” facts are scattered in a vast literature as folklore, sometimes with proofs available only in the complex analytic category. This book is an attempt to ?ll such a gap, at least p- tially.
 

Was andere dazu sagen - Rezension schreiben

Es wurden keine Rezensionen gefunden.

Inhalt

Terminology and notation
1
Infinitesimal deformations 9
8
Formal deformation theory
37
Examples of deformation functors 103
102
Hilbert and Quot schemes
187
A Flatness
269
B Differentials
279
Smoothness
293
Complete intersections 305
304
E Functorial language
313
References 321
320
List of symbols
329
Urheberrecht

Andere Ausgaben - Alle anzeigen

Häufige Begriffe und Wortgruppen

Über den Autor (2007)

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.

Bibliografische Informationen