說明 
1 online resource (xii, 420 pages) : digital, PDF file(s) 

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系列 
London Mathematical Society lecture note series ; 345 

London Mathematical Society lecture note series ; 345

附註 
Title from publisher's bibliographic system (viewed on 05 Oct 2015) 

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 

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 
主題 
Geometry, Algebraic


Geometry, Analytic

Alt Title 
Algebraic & Analytic Geometry 
