Complex Analytic Sets: 46 (Mathematics and its Applications, 46) - Hardcover

Chirka, E.M.

Hardcover

ISBN 10: 0792302346 ISBN 13: 9780792302346

Publisher: Springer, 1989

Synopsis

The theory of complex analytic sets is part of the modern geometrical theory of functions of several complex variables. A wide circle of problems in multidimensional complex analysis, related to holomorphic functions and maps, can be reformulated in terms of analytic sets. In these reformulations additional phenomena may emerge, while for the proofs new methods are necessary. (As an example we can mention the boundary properties of conformal maps of domains in the plane, which may be studied by means of the boundary properties of the graphs of such maps.)

The theory of complex analytic sets is a relatively young branch of complex analysis. Basically, it was developed to fulfill the need of the theory of functions of several complex variables, but for a long time its development was, so to speak, within the framework of algebraic geometry - by analogy with algebraic sets. And although at present the basic methods of the theory of analytic sets are related with analysis and geometry, the foundations of the theory are expounded in the purely algebraic language of ideals in commutative algebras.

In the present book I have tried to eliminate this noncorrespondence and to give a geometric exposition of the foundations of the theory of complex analytic sets, using only classical complex analysis and a minimum of algebra (well-known properties of polynomials of one variable). Moreover, it must of course be taken into consideration that algebraic geometry is one of the most important domains of application of the theory of analytic sets, and hence a lot of attention is given in the present book to algebraic sets. 

About this title

Synopsis

Monograph providing advanced graduate students and other researchers with an account of the zero sets of holomorphic functions of several complex variables, which are studied here from a geometric (rather than an algebraic) point of view, with emphasis particularly on the global aspects of the theory. The approach is modern, and many of the results

Edition details

• Publisher: Springer
• Publication date: 1989
• Language: English
• ISBN 10: 0792302346
• ISBN 13: 9780792302346
• Binding: Hardcover
• Number of pages: 392