| Summary: | This textbook is a strong addition to existing introductory literature on algebraic geometry. The author’s treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields. Unique features of this textbook: - Contains a rapid introduction to complex algebraic geometry - Includes background material on topology, manifold theory and sheaf theory - Analytic and algebraic approaches are developed somewhat in parallel The presentation is easy going, elementary, and well illustrated with examples. “Algebraic Geometry over the Complex Numbers” is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory
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