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Complex Analytic Sets

  • Chapter
Introduction to Complex Analysis

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 7))

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Abstract

The theory of complex analytic sets is part of the modern geometric theory of functions of several complex variables. Traditionally, the presentation of the foundations of the theory of analytic sets is introduced in the algebraic language of ideals in Noetherian rings as, for example, in the books of Hervé [23] or Gunning-Rossi [19]. However, the modern methods of this theory, the principal directions and applications, are basically related to geometry and analysis (without regard to the traditional direction which is essentially related to algebraic geometry). Thus, at the beginning of this survey, the geometric construction of the local theory of analytic sets is presented. Its foundations are worked out in detail in the book of Gunning and Rossi [19] via the notion of analytic cover which together with analytic theorems on the removal of singularities leads to the minimum of algebraic apparatus necessary in order to get the theory started.

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  1. E. M. Chirka
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Chirka, E.M. (1997). Complex Analytic Sets. In: Introduction to Complex Analysis. Encyclopaedia of Mathematical Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61525-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-61525-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63005-0

  • Online ISBN: 978-3-642-61525-2

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