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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