Principles of Algebraic Geometry

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9780471050599: Principles of Algebraic Geometry

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.

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From the Back Cover:

Other volumes in the Pure and Applied Mathematics series— The Algebraic Structure of Group Rings Donald S. Passman This book offers a comprehensive, self-contained treatment of group rings of infinite groups. It begins with basic definitions and contains background material on group theory and ring theory. Major topics considered include: the trace map, the augmentation ideal and dimension subgroups, linear and polynomial identities and their relationship to the center, semisimplicity and primitivity, polycyclic-by-finite groups and Philip Hall’s problem, zero divisors, and isomorphism questions. 1977 Topological Uniform Structures Warren Page Here is an overall unifying theme of topologies compatible with increasingly enriched algebraic structures, showing the rich interplay among mathematics’ diverse areas. It studies mathematics as a structured, coherent, and harmonious whole, giving a detailed examination of uniform spaces, topological groups, topological vector spaces, topological algebras, and abstract harmonic analysis. Also includes a section on topological vector-valued measure spaces and numerous problems and examples. The text is virtually self-contained, presenting detailed proofs, stressing readability and motivation, and covering much advanced material. 1978 Applied Abstract Analysis Jean-Pierre Aubin Discusses all the main theorems of topology by introducing and studying principal topics in the elementary framework of metric spaces. Considers various applications in differential equations, dynamic systems, game theory, and economics, illustrating the advantages of using an abstract approach to solve problems of a more concrete nature. Also includes a concise review of essential results, a set of exercises and problems, and a terminological index. 1977

From the Inside Flap:

Changes in algebraic geometry have made it a subject that, over the past few years, has become increasingly inaccessible to all but the specialist. This comprehensive, self-contained treatment presents some of the main, general results of the theory accompanied by (and with emphasis on) their applications to the study of interesting examples and to the development of computational tools. It establishes a geometric intuition and a working facility with specific geometric practices, providing mathematicians and physicists with a greater accessibility to the field. The effective utilization of the techniques of elementary complex analysis and topology synthesize the classical and the modern—the geometric and the abstract-into a cohesive presentation. Coverage ranges from analytic to geometric along classical lines. Basic techniques and results of complex manifold theory are treated, focusing on results applicable to projective varieties. Further discussions include the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex, and special topics in complex manifolds.

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