Algebraic and Analytic Geometry / Amnon Neeman.

By: Neeman, Amnon [author.]Material type: TextTextSeries: London Mathematical Society Lecture Note Series ; no. 345Publisher: Cambridge : Cambridge University Press, 2007Description: 1 online resource (434 pages) : digital, PDF file(s)Content type: text Media type: computer Carrier type: online resourceISBN: 9780511800443 (ebook)Other title: Algebraic & Analytic GeometrySubject(s): Geometry, Algebraic | Geometry, AnalyticAdditional physical formats: Print version: : No titleDDC classification: 516.3 Online resources: Click here to access online Summary: 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.
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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.

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