Complex Analytic Sets
Complex Analytic Sets
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DOI：
10.1007/978-3-642-61525-2_3
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发表时间：
1989-07
期刊：
影响因子：
--
通讯作者：
E. Chirka
中科院分区：
文献类型：
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作者：
E. Chirka
复解析集理论是多复变函数的现代几何理论的一部分。传统上，解析集理论的基础是用诺特环中理想的代数语言来介绍的，例如在Hervé [23]或Gunning-Rossi [19]的书中。然而，这个理论的现代方法，主要方向和应用，基本上与几何和分析有关（不考虑传统的方向，基本上与代数几何有关）。因此，在本调查的开始，几何结构的局部理论的解析集。它的基础在Gunning和Rossi [19]的书中通过解析覆盖的概念详细阐述，该概念与关于去除奇点的解析定理一起导致理论开始所需的代数装置的最小化。
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.