Algebraic and Analytic Geometry

Algebraic and Analytic Geometry

by Amnon Neeman
     
 

ISBN-10: 0521709830

ISBN-13: 9780521709835

Pub. Date: 09/13/2007

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521709835
Publisher:
Cambridge University Press
Publication date:
09/13/2007
Series:
London Mathematical Society Lecture Note Series, #345
Edition description:
New Edition
Pages:
434
Product dimensions:
5.98(w) x 8.98(h) x 0.98(d)

Table of Contents

Foreword; 1. Introduction; 2. Manifolds; 3. Schemes; 4. The complex topology; 5. The analytification of a scheme; 6. The high road to analytification; 7. Coherent sheaves; 8. Projective space - the statements; 9. Projective space - the proofs; 10. The proof of GAGA; Appendix. The proofs concerning analytification; Bibliography; Glossary; Index.

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