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Algebraic and Analytic Geometry : London Mathematical Society Lecture Note Series - Amnon Neeman

Algebraic and Analytic Geometry

London Mathematical Society Lecture Note Series

Paperback

Published: 13th September 2007
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This textbook, for an undergraduate course in modern algebraic geometry, recognizes that the typical undergraduate curriculum contains a great deal of analysis and, by contrast, little algebra. Because of this imbalance, it seems most natural to present algebraic geometry by highlighting the way it connects algebra and analysis; the average student will probably be more familiar and more comfortable with the analytic component. The book therefore focuses on Serre's GAGA theorem, which perhaps best encapsulates the link between algebra and analysis. GAGA provides the unifying theme of the book: we develop enough of the modern machinery of algebraic geometry to be able to give an essentially complete proof, at a level accessible to undergraduates throughout. The book is based on a course which the author has taught, twice, at the Australian National University.

All in all, the book under review is a masterpiece of expository writing in modern algebraic geometry. It is exactly what the author promised: no comprehensive text to train future algebraic geometers, but rather an attempt to convince students of the fascinating beauty, the tremendous power, and the high value of the methods of algebraic and analytic geometry ... The author has reached his declared goal in an admirable, truly brilliant manner. His lucid exposition of these modern, fairly advanced topics in the field for beginners breathes his passion for the subject and for grippingly teaching it, and his style of writing bespeaks a good sympathetic understanding of students and their needs. Numerous synoptic sections, asides for the expert reader, and additional remarks help the student grasp the vast material thoroughly, and both the careful glossary and the detailed index facilitate active work with this highly inspiring book. Also, the author makes concrete, instructive proposals for how to use his text for different variants of self-study or teaching, which is particularly useful as its current extended contents now offer far more than can be covered in a one-semester course ... It remains to wish that this very special introduction to the realm of(complex)algebraic geometry finds deserved wide-spread interest within the mathematical community. Werner Kleinert, Zentralblatt MATH

Foreword
Introduction
Manifolds
Schemes
The complex topology
The analytification of a scheme
The high road to analytification
Coherent sheaves
Projective space - the statements
Projective space - the proofs
The proof of GAGA;
Appendix
The proofs concerning analytification
Bibliography
Glossary
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521709835
ISBN-10: 0521709830
Series: London Mathematical Society Lecture Note Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 434
Published: 13th September 2007
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.5
Weight (kg): 0.63