霍奇理论与复代数几何 2本套装 英文原版 Hodge Theory and Complex Algebraic Geometry Claire Voisin

基本信息

Format Paperback | 696pages

Dimensions 154 x 227 x 37mm | 1100g

Publication date 18 Jan 2012

Publisher Cambridge University Press

Language English

ISBN10 0521718023

ISBN13 P97805217180282109002

页面参数仅供参考，具体以实物为准

目录

1.9780521718011 霍奇理论与复代数几何 第一卷 Hodge Theory and Complex Algebraic Geometry I

2.9780521718028 霍奇理论与复代数几何 第二卷 Hodge Theory and Complex Algebraic Geometry II

书籍简介

1.两卷中的第一卷提供了对Kaehlerian几何和霍奇结构的现代介绍。书以复变量、复流形、全纯向量束、束束和上同调论的基本材料开始，后者比通常的几何处理方法更加理论化。然后，作者证明了卡勒恒等式，从而引出了hard Lefschetz定理和Hodge指数定理。

这本书以霍奇分解定理而告终。从几个方面研究了这些结果的意义。这本书完全独立，对学生来说是理想的，它的内容讲述了霍奇理论和复杂的代数几何，这是由P. Deligne和S. Bloch发展讨论而得。

文本由练习补充，这些练习在复杂代数几何中提供了有用的结果。

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem.

The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P.Griffiths and his school, by P. Deligne, and by S. Bloch.

The text is complemented by exercises which provide useful results in complex algebraic geometry.

2.2003年第二卷关于Kaehlerian几何学和Hodge理论的论述从代数簇的拓扑开始。超平面截面上的Lefschetz定理的证明，Lefschetz铅笔的Picard-Lefschetz研究，以及关于Leray谱序列和全局不变环的退化的Deligne定理。第二部分的主要结果是广义诺瑟尔-左撇子定理，阿贝尔-雅可比图的一般平凡性，以及最重要的诺瑟尔-左撇子连通定理。

本书的最后一部分致力于霍奇理论和代数循环之间的关系。本书以阿贝尔变种的循环为例作结，其中举例说明了布洛赫和比维尔的一些结果。文本由练习补充，在复杂的代数几何中给出有用的结果。

它将受到代数和微分几何研究人员的欢迎。

The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above.

The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry.

It will be welcomed by researchers in both algebraic and differential geometry

作者简介

克莱尔·沃辛(Claire Voisin)是法国高等科学研究学院的教授

Claire Voisin is a Professor at the Institut des Hautes Études Scientifiques, France