Algebraic and Analytic Geometry
Algebraic and Analytic Geometry
£91.99
GBPThis 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.
- Builds machinery of algebraic geometry upon what students already know well
- Modern approach - focusses on Serre's GAGA theorem
- Accessible to undergraduates - many examples and exercises throughout the text allow the reader to understand the abstract material at a concrete level
Reviews & endorsements
'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.' Werner Kleinert, Zentralblatt MATH
'… written in a very understandable way, with a lot of details and with many remarks and comments helping to develop intuition for the field. It is an extraordinary book …' European Mathematical Society Newsletter
Product details
September 2007Paperback
9780521709835
434 pages
229 × 152 × 25 mm
0.602kg
101 b/w illus. 20 exercises
Available
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.
