Complex Analytic Cycles II: The Cycle Space
暫譯: 複雜分析循環 II：循環空間
Barlet, Daniel, Magnússon, Jón
- 出版商: Springer
- 出版日期: 2025-06-20
- 售價: $7,050
- 貴賓價: 9.5 折 $6,698
- 語言: 英文
- 頁數: 644
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031848446
- ISBN-13: 9783031848445
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商品描述
This book is the second volume of a work on complex analytic cycles and the results, stated without proof in the first volume, are proved here. It begins with the construction of the reduced complex space formed by all compact cycles of a given complex space. Following this construction the main subjects of the book are:
- Fundamental class of a cycle and relative fundamental class of an analytic family of cycles
- Intersection theory with parameters on complex manifolds and more generally on nearly smooth complex spaces
- Holomorphic currents on reduced complex spaces
- Chow varieties and cycle spaces of quasi-projective complex spaces
- Natural morphism from the Douady space to the cycle space
- Holomorphic convexity in cycle spaces and integration of $\bar{partial}$-cohomology classes on cycles
- Strong Kählerianity of cycle spaces of Kähler manifolds
- Numerous important applications of cycle space theory
Preliminaries needed in the book in addition to the material of the first volume, for instance sheaf cohomology with support, are explained in detail, making this two-volume work quite self-contained. The French version of the present book was published in 2020 by the French Mathematical Society in the series Cours Spécialisés and during the translation process the authors have in many ways improved the original version.
商品描述(中文翻譯)
這本書是關於複雜分析循環的作品的第二卷，第一卷中未證明的結果在此處得到了證明。書中首先構建了由給定複雜空間的所有緊湊循環所形成的簡化複雜空間。接下來，書中的主要主題包括：
- 循環的基本類別及分析循環族的相對基本類別
- 在複雜流形上的參數交集理論，以及更一般地在近光滑複雜空間上的交集理論
- 在簡化複雜空間上的全純流
- Chow 變體及準射影複雜空間的循環空間
- 從 Douady 空間到循環空間的自然態射
- 循環空間中的全純凸性及在循環上的 $\bar{partial}$-上同調類的積分
- Kähler 流形的循環空間的強 Kähler 性
- 循環空間理論的眾多重要應用
除了第一卷的材料外，本書還詳細解釋了所需的初步知識，例如帶支撐的層上同調，使這部兩卷本的作品相當自足。本書的法文版於2020年由法國數學學會在 Cours Spécialisés 系列中出版，在翻譯過程中，作者在許多方面改進了原始版本。
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 thèse d'État 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 (Analysis and Complex Geometry) from 1998 to 2003 and his chair was renewed for five years in 2003. Since 2011 he has been professor emeritus at the Institute of Elie Cartan at the University of Lorraine.
Jón Magnússon finished a B.Sc. in mathematics at the University of Iceland in 1976 and obtained 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.
作者簡介(中文翻譯)
丹尼爾·巴爾特（Daniel Barlet）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月辯護其國家論文（thèse d'État）。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（French Mathematical Society）會長（92/94），並於1998年至2003年當選法國大學院（Institut Universitaire de France）的高級成員（分析與複雜幾何），其職位於2003年續任五年。自2011年以來，他一直是洛林大學艾利·卡坦研究所（Institute of Elie Cartan）的名譽教授。
約恩·馬格努森（Jón Magnússon）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。自那時以來，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（cycle space theory）。
