Deformations of Algebraic Schemes

Edoardo Sernesi

ISBN 10: 3642067875 / ISBN 13: 9783642067877

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg, 2010

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783642067877

Bibliographic Details

• Title: Deformations of Algebraic Schemes
• Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg
• Publication Date: 2010
• Language: English
• ISBN 10: 3642067875
• ISBN 13: 9783642067877
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 20D millimeters 235 millimeters width by 155 millimeters height by 20 millimeters depth
• Weight: 540 grams

About this title

Synopsis

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.

About the Author

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.