Principles of Algebraic Geometry

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.Griffiths, Phillip is the author of 'Principles of Algebraic Geometry' with ISBN 9780471327929 and ISBN 0471327921.