Deformations of Algebraic Schemes | Buch

Cover: 9783540306085 | Deformations of Algebraic Schemes | Edoardo Sernesi | Buch | xi | 2006

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Beschreibung

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.

Über den Autor

Edoardo Sernesi - vita

Present position:
Professore ordinario di Geometria, FacoltÃ di Scienze MFN, UniversitÃ Roma Tre

Education:
- Laurea in Matematica- UniversitÃ di Roma, 1969
- Ph.D. in Mathematics - Brandeis University, 1976

Professional experience:
- Assistente ordinario di Geometria, UniversitÃ di Ferrara, 1974-1980.
- Professore straordinario di Geometria UniversitÃ di Roma ``La Sapienza", 1980-1983.
- Professore ordinario di Geometria UniversitÃ di Roma ``La Sapienza", 1983-1992.
- Professore ordinario di Geometria UniversitÃ Roma Tre, from 1992.

Zusammenfassung

This book brings together for the first time some results so far scattered across a vast literature

Fills a long-standing gap in the literatur, where no reference book existed and the results had become "folklore"

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2006
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Grundlehren der mathematischen Wissenschaften
Inhalt:	xi 342 S.
ISBN-13:	9783540306085
ISBN-10:	3540306080
Sprache:	Englisch
Herstellernummer:	11371335
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Sernesi, Edoardo
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Grundlehren der mathematischen Wissenschaften
Maße:	241 x 160 x 25 mm
Von/Mit:	Edoardo Sernesi
Erscheinungsdatum:	06.07.2006
Gewicht:	0,699 kg

Artikel-ID: 102262792