Complex Analytic Sets

Name: Complex Analytic Sets
Brand: Springer
SKU: 9780792302346
Price: 10900.0 INR
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by E. M. Chirka

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ISBN13: 9780792302346
Binding: Hardcover
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: July 31, 1989
Pages: 372
Original Price: EUR 149.99
Language: English
Edition: 1989
Item Weight: 731 grams
BISAC Subject(s): Calculus, Mathematical Analysis, and Geometry / Algebraic

About The Book

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.

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