2007/09/13 by Amnon Neeman · 2 citations
Mathematics · #Mathematics and Applications #Algebra over a field #Theme (computing) #Algebraic geometry #Analytic geometry #Abstract algebra #Algebraic number #Curriculum #Mathematics #Geometry #Algebraic expression #Computer science #Mathematics education #Calculus (dental) #Pure mathematics #Pedagogy #Sociology
paper · doi:10.1017/cbo9780511800443
openalex publication_date 2007/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
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.