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Complex Analytic Cycles II : The Cycle Space.
・ISBN 978-3-031-84847-6 paper EUR 179.99
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| 著者・編者 | Barlet, Daniel / Magnusson, Jon, |
|---|---|
| シリーズ | (Grundlehren der mathematischen Wissenschaften) |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2026 |
| ページ数 | 640 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-25974＞ |
解説
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 Kaehlerianity of cycle spaces of Kaehler 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 Specialises and during the translation process the authors have in many ways improved the original version.