点击选择搜索分类
首页 - 社会调查- 正文
☆☆☆☆☆
||
[德] 霍布西兹 著
出版社: 世界图书出版公司 ISBN:9787510004636 版次:1 商品编码:10184579 包装:平装 外文名称:Complex Geomety:An Introduction 开本:24开 出版时间:2010-01-01 用纸:胶版纸 页数:309 正文语种:英语
1.1 Holomorphic Functions of Several Variables
1.2 Complex and Hermitian Structures
1.3 Differential Forms
2 Complex Manifolds
2.1 Complex Manifolds: Definition and Examples
2.2 Holomorphic Vector Bundles
2.3 Divisors and Line Bundles
2.4 The Projective Space
2.5 Blow-ups
2.6 Differential Calculus on Complex Manifolds
3 Kahler Manifolds
3.1 Kahler Identities
3.2 Hodge Theory on Kahler Manifolds
3.3 Lefschetz Theorems
Appendix
3.A Formality of Compact Kahler Manifolds
3.B SUSY for Kahler Manifolds
3.C Hodge Structures
4 Vector Bundles
4.1 Hermitian Vector Bundles and Serre Duality
4.2 Connections
4.3 Curvature
4.4 Chern Classes
Appendix
4.A Levi-Civita Connection and Holonomy on Complex Manifolds
4.B Hermite-Einstein and Kahler-Einstein Metrics
5 Applications of Cohomology
5.1 Hirzebruch-Riemann-Roch Theorem
5.2 Kodaira Vanishing Theorem and Applications
5.3 Kodaira Embedding Theorem
Deformations of Complex Structures
6.1 The Maurer-Cartan Equation
6.2 General Results
Appendix
6.A dGBV-Algebras
A Hodge Theory on Differentiable Manifolds
B Sheaf Cohomology
References
Index
Complex geometry, as presented in this book, studies the geometry of(mostly compact) complex manifolds. A complex manifold is a differentiablemanifold endowed with the additional datum of a complex structure which ismuch more rigid than the geometrical structures in differential geometry. Dueto this rigidity, one is often able to describe the geometry of complex manifoldsin very explicit terms. E.g. the important class of projective manifolds can, inprinciple, be described as zero sets of polynomials.
Yet, a complete classification of all compact complex manifolds is toomuch to be hoped for. Complex curves can be classified in some sense (in-volving moduli spaces etc.), but already the classification of complex surfacesis tremendously complicated and partly incomplete.
In this book we will concentrate on more restrictive types of complexmanifolds for which a rather complete theory is in store and which are alsorelevant in the applications. A prominent example are Calabi-Yau manifolds,which play a central role in questions related to mirror symmetry. Often,interesting complex manifolds are distinguished by the presence of specialRiemannian metrics. This will be one of the central themes throughout thistext. The idea is to study cases where the Riemannian and complex geometryon a differentiable manifold are not totally unrelated.
复几何导论(英文版) [Complex Geomety:An Introduction] 电子书 下载 mobi epub pdf txt
复几何导论(英文版) [Complex Geomety:An Introduction]-so88
复几何导论(英文版) [Complex Geomety:An Introduction] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[德] 霍布西兹 著
出版社: 世界图书出版公司 ISBN:9787510004636 版次:1 商品编码:10184579 包装:平装 外文名称:Complex Geomety:An Introduction 开本:24开 出版时间:2010-01-01 用纸:胶版纸 页数:309 正文语种:英语
内容简介
Complex geometry is a highly attractive branch of modern mathematics that has witnessed many years of active and successful research and that has re- cently obtained new impetus from physicists interest in questions related to mirror symmetry. Due to its interactions with various other fields (differential, algebraic, and arithmetic geometry, but also string theory and conformal field theory), it has become an area with many facets. Also, there are a number of challenging open problems which contribute to the subjects attraction. The most famous among them is the Hodge conjecture, one of the seven one-million dollar millennium problems of the Clay Mathematics Institute. So, it seems likely t at this area will fascinate new generations for many years to come.内页插图
目录
1 Local Theory1.1 Holomorphic Functions of Several Variables
1.2 Complex and Hermitian Structures
1.3 Differential Forms
2 Complex Manifolds
2.1 Complex Manifolds: Definition and Examples
2.2 Holomorphic Vector Bundles
2.3 Divisors and Line Bundles
2.4 The Projective Space
2.5 Blow-ups
2.6 Differential Calculus on Complex Manifolds
3 Kahler Manifolds
3.1 Kahler Identities
3.2 Hodge Theory on Kahler Manifolds
3.3 Lefschetz Theorems
Appendix
3.A Formality of Compact Kahler Manifolds
3.B SUSY for Kahler Manifolds
3.C Hodge Structures
4 Vector Bundles
4.1 Hermitian Vector Bundles and Serre Duality
4.2 Connections
4.3 Curvature
4.4 Chern Classes
Appendix
4.A Levi-Civita Connection and Holonomy on Complex Manifolds
4.B Hermite-Einstein and Kahler-Einstein Metrics
5 Applications of Cohomology
5.1 Hirzebruch-Riemann-Roch Theorem
5.2 Kodaira Vanishing Theorem and Applications
5.3 Kodaira Embedding Theorem
Deformations of Complex Structures
6.1 The Maurer-Cartan Equation
6.2 General Results
Appendix
6.A dGBV-Algebras
A Hodge Theory on Differentiable Manifolds
B Sheaf Cohomology
References
Index
前言/序言
Complex geometry is a highly attractive branch of modern mathematics thathas witnessed many years of active and successful research and that has recently obtained new impetus from physicists interest in questions related tomirror symmetry. Due to its interactions with various other fields (differential,algebraic, and arithmetic geometry, but also string theory and conformal fieldtheory), it has become an area with many facets. Also, there are a number ofchallenging open problems which contribute to the subjects attraction. Themost famous among them is the Hodge conjecture, one of the seven one-milliondollar millennium problems of the Clay Mathematics Institute. So, it seemslikely that this area will fascinate new generations for many years to come.Complex geometry, as presented in this book, studies the geometry of(mostly compact) complex manifolds. A complex manifold is a differentiablemanifold endowed with the additional datum of a complex structure which ismuch more rigid than the geometrical structures in differential geometry. Dueto this rigidity, one is often able to describe the geometry of complex manifoldsin very explicit terms. E.g. the important class of projective manifolds can, inprinciple, be described as zero sets of polynomials.
Yet, a complete classification of all compact complex manifolds is toomuch to be hoped for. Complex curves can be classified in some sense (in-volving moduli spaces etc.), but already the classification of complex surfacesis tremendously complicated and partly incomplete.
In this book we will concentrate on more restrictive types of complexmanifolds for which a rather complete theory is in store and which are alsorelevant in the applications. A prominent example are Calabi-Yau manifolds,which play a central role in questions related to mirror symmetry. Often,interesting complex manifolds are distinguished by the presence of specialRiemannian metrics. This will be one of the central themes throughout thistext. The idea is to study cases where the Riemannian and complex geometryon a differentiable manifold are not totally unrelated.
复几何导论(英文版) [Complex Geomety:An Introduction] 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 爱心天使-芭比魅力百变沙画秀
- 中国历史上的大辟疆 9787802233553
- 澳洲鸟类 9787568233187
- 离线 科幻:Imaging Technology
- 什么是科学(荣获“大众喜欢的50种图书”) 吴国盛,博集天卷 出品
- 羊皮卷全集(珍藏版) [Scrolls for Success]
- 探秘海底世界-小学生着迷的第一堂自然课
- 星空探奇 9787302407386
- 风云漫话:王章敏气象科普作品选
- 从行动开始:自我管理的科学
- 揭开世界文化之谜
- 现代科学技术与爱因斯坦
- 推动丛书综合系列:复杂 [美] 梅拉妮米歇尔
- 开一家赚钱的个性小店大全集
- {RT}神奇的物理之旅:双色插图版-Kamil Fadel 机械工业出版社 9787111