Analytic Cycles of Finite Type
暫譯: 有限型分析循環

Barlet, Daniel, Magnússon, Jón Ingólfur

Analytic Cycles of Finite Type
  • 出版商: Springer
  • 出版日期: 2025-08-02
  • 售價: $3,010
  • 貴賓價: 9.5 折 $2,860
  • 語言: 英文
  • 頁數: 139
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031964055
  • ISBN-13: 9783031964053
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

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商品描述

This book highlights the use of non-compact analytic cycles in complex geometry. The main focus is on analytic families of cycles of finite type, in other words, cycles which have only finitely many irreducible components. It is shown how the space of all cycles of finite type in a given complex space, endowed with a weak analytic structure, can be used in many ways as the reduced complex space of all compact cycles in the given space. Several illustrative and enlightening examples are provided, as well as applications, giving life to the theory. The exposition includes a characterization of quasi-proper holomorphic maps which admit a geometric flattening, a proof of an existence theorem for meromorphic quotients with respect to a large class of analytic equivalence relations, and a generalization of the Stein factorization to a variety of holomorphic maps. In addition, a study is made of the behavior of analytic families of finite type cycles when they are restricted to Zariski open subsets and extended across analytic subsets.

Aimed at researchers and graduate students with an interest in complex or algebraic geometry, the book is adequately self-contained, the basic notions are explained and suitable references are given for auxiliary results that are used in the text.

商品描述(中文翻譯)

這本書強調在複雜幾何中使用非緊湊解析循環。主要焦點是有限型的循環的解析族，換句話說，就是只有有限多不可約組件的循環。書中展示了如何利用給定複雜空間中所有有限型循環的空間，並賦予其弱解析結構，來以多種方式作為該空間中所有緊湊循環的簡化複雜空間。提供了幾個具啟發性和說明性的例子，以及應用，為理論注入生命。內容包括對於允許幾何展平的準適當全純映射的特徵描述，對於一大類解析等價關係的有理商存在定理的證明，以及對全純映射的斯坦因分解的推廣。此外，還研究了有限型循環的解析族在限制於 Zariski 開子集時的行為，以及在解析子集上擴展的情況。

本書針對對複雜或代數幾何感興趣的研究人員和研究生，內容自成體系，基本概念有詳細解釋，並提供了適當的參考資料以輔助文本中使用的輔助結果。

作者簡介

Daniel Barlet studied mathematics at the ENS Ulm (Paris) from 1966 to 1970. After his graduation he became assistant professor at the University of Paris VII, where he defended his these d'etat in December 1974. From 1976 to 2011 he was professor at the University of Nancy I, which is today a part of the University of Lorraine. He was president of the French Mathematical Society (92/94) and was elected as a senior member of the Institut Universitaire de France (Complex Analysis and Complex Geometry) from 1998 to 2003. His chair was renewed for a further five years in 2003. Since 2011 he has been professor emeritus at the Institute of Elie Cartan at the University of Lorraine. Jón Ingólfur Magnússon obtained a B.Sc. in mathematics at the University of Iceland in 1976 and a doctoral degree in mathematics from the University of Paris VII (Jussieu) in 1981. Since then, he has been working, first as a research mathematician and later as a professor, at the University of Iceland. In 2023 he became a professor emeritus at the University of Iceland. His research interests are mainly in cycle space theory. The authors wrote a two volume work on analytic cycles in complex spaces which was published by the French Mathematical Society (Cours Spécialisés 22 and 27) in 2014 and 2020. An improved English version of the first volume was published by Springer (Grundlehren der mathematischen Wissenschaften 356) in 2019 and an English version of the second volume will soon be published in the same series.

作者簡介(中文翻譯)

丹尼爾·巴爾特於1966年至1970年在巴黎高等師範學院（ENS Ulm）學習數學。畢業後，他成為巴黎第七大學的助理教授，並於1974年12月辯護他的博士論文。從1976年到2011年，他在南錫大學（University of Nancy I）任教，該校如今是洛林大學（University of Lorraine）的一部分。他曾擔任法國數學學會的會長（1992/1994），並於1998年至2003年被選為法國大學院（Institut Universitaire de France）的高級成員（複雜分析與複雜幾何）。他的職位在2003年續聘五年。自2011年以來，他一直是洛林大學艾利·卡爾坦研究所的名譽教授。約恩·英戈爾夫·馬格努森於1976年在冰島大學獲得數學學士學位，並於1981年在巴黎第七大學（Jussieu）獲得數學博士學位。自那時起，他一直在冰島大學工作，最初擔任研究數學家，後來成為教授。2023年，他成為冰島大學的名譽教授。他的研究興趣主要集中在循環空間理論上。 這兩位作者撰寫了有關複雜空間中解析循環的兩卷作品，該作品由法國數學學會於2014年和2020年出版（Cours Spécialisés 22 和 27）。第一卷的改進英文版於2019年由施普林格（Springer）出版（Grundlehren der mathematischen Wissenschaften 356），第二卷的英文版將很快在同一系列中出版。

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