Deformations of Algebraic Schemes

Language: English

Published by Springer, 2010

3642067875 / 9783642067877

Series: Book 55 of 184 - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge/A Series of Modern Surveys in Mathematics

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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

Title
Deformations of Algebraic Schemes
Author
Edoardo Sernesi
Publisher
Springer
Publication year
2010
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3642067875
ISBN 13
9783642067877
Item weight
540 grams
Dimensions
235x155x20 mm
Series
Book 55 of 184: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge/A Series of Modern Surveys in Mathematics

AHA-BUCH GmbH

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