紧复曲面.第2版:英文(影印版)
基本信息
- 原书名: Compact Complex Surfaces
- 原出版社: Springer
- 作者: W. Barth K. Hulek Chris Peters A.van de Ven
- 出版社:世界图书出版公司
- ISBN:9787510033018
- 上架时间:2011-8-8
- 出版日期:2011 年4月
- 开本:24开
- 页码:436
- 版次:2-1
- 所属分类:
数学 > 几何及拓扑 > 综合
编辑推荐
读者评论:“可以说如果学代数几何没念过这本书,甚至是学几何没念过这本书,可以考虑换行,是百年难得一见的好书。”
内容简介回到顶部↑
《紧复曲面.第2版英文(影印版)》是一部非常好的学习代数曲面的书,提供了复曲面分类的复解析方法。此书是从复代数几何角度研究复曲面的大全类书籍,从初等入门到高深前沿都有涉及。这本书是经典中的经典,讲的是代数曲面的各种专题,每个章节都写的无限完美。内容包括曲面里的曲线,相交数,霍奇分解,pojectivity,有理曲面分类,Kodaira分类,general 曲面,K3&Enrique曲面。此书新版的最后两章写的尤其好,一是 K3 曲面;另一个是 Doanaldson 和 Seiber Witten 理论,后者是来自模空间的不变量理论,都是现在热门的专题。有位读者这么说:“可以说如果学代数几何没念过这本书,甚至是学几何没念过这本书,可以考虑换行,是百年难得一见的好书。“可见这《紧复曲面.第2版英文(影印版)》书在该领域具有举足轻重的地位。
目录回到顶部↑
《紧复曲面.第2版英文(影印版)》
introduction
historical note
the contents of the book
standard notation
i. preliminaries
topology and algebra
1. notation and basic facts
2. some properties of bilinear forms
3. vector bundles, characteristic classes and the index theorem
complex manifolds
4. basic concepts and facts
5. holomorphic vector bundles, serre duality and riemann-roch
6. line bundles and divisors
7. algebraic dimension and kodaira dimension
general analytic geometry
8. complex spaces
9. the a-process
10. deformations of complex manifolds
differential geometry of complex manifolds
introduction
historical note
the contents of the book
standard notation
i. preliminaries
topology and algebra
1. notation and basic facts
2. some properties of bilinear forms
3. vector bundles, characteristic classes and the index theorem
complex manifolds
4. basic concepts and facts
5. holomorphic vector bundles, serre duality and riemann-roch
6. line bundles and divisors
7. algebraic dimension and kodaira dimension
general analytic geometry
8. complex spaces
9. the a-process
10. deformations of complex manifolds
differential geometry of complex manifolds
前言回到顶部↑
Preface to the Second Edition
In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants.Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces.
Other developments include the systematic use of nef-divisors (in ac-cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kaihler structures on surfaces,and Reider's new approach to adjoint mappings.
All these developments have been incorporated in the present edition,though the Donaldson and Seiberg-Witten theory only by way of examples.Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.
We gratefully acknowledge the support of various bodies which helpedus prepare this new edition; in particular the following grants and institu-tions: EAGER (European Algebraic Geometry Research Network) and the DFG (Deutsche Forschungsgemeinschaft) as well as the universities of Essen,Grenoble, Hannover and Leiden for the hospitality we were offered at various occasions. Our thanks go to those who have read and commented on parts of the manuscript: R. Eckert, C. Erdenberger, M. Friedland, A. Gathmann,M. LSnne, K. Ludwig, John D. McCarthy, M. Schiitt, J. Spandaw and H.Verrill. We are in particular grateful to J.-P. Demailly, L. Bonavero and A.Teleman for all the advice they offered which helped us to understand some of the hard analysis needed in various new parts of the book.
Special thanks also to Mme. A. Guttin-Lombard, who efficiently prepared a major part of the book, and to Mrs. S. Guttner for the careful typing of several chapters.
Grenoble/Erlangen/Hannover/Leiden, July 2003
W. Barth
K. Hulek
C. Peters
A. Van de Ven
In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants.Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces.
Other developments include the systematic use of nef-divisors (in ac-cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kaihler structures on surfaces,and Reider's new approach to adjoint mappings.
All these developments have been incorporated in the present edition,though the Donaldson and Seiberg-Witten theory only by way of examples.Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.
We gratefully acknowledge the support of various bodies which helpedus prepare this new edition; in particular the following grants and institu-tions: EAGER (European Algebraic Geometry Research Network) and the DFG (Deutsche Forschungsgemeinschaft) as well as the universities of Essen,Grenoble, Hannover and Leiden for the hospitality we were offered at various occasions. Our thanks go to those who have read and commented on parts of the manuscript: R. Eckert, C. Erdenberger, M. Friedland, A. Gathmann,M. LSnne, K. Ludwig, John D. McCarthy, M. Schiitt, J. Spandaw and H.Verrill. We are in particular grateful to J.-P. Demailly, L. Bonavero and A.Teleman for all the advice they offered which helped us to understand some of the hard analysis needed in various new parts of the book.
Special thanks also to Mme. A. Guttin-Lombard, who efficiently prepared a major part of the book, and to Mrs. S. Guttner for the careful typing of several chapters.
Grenoble/Erlangen/Hannover/Leiden, July 2003
W. Barth
K. Hulek
C. Peters
A. Van de Ven

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