復幾何導論 pdf epub mobi txt 電子書下載2025

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出版者:世界圖書齣版公司

作者:[德] Daniel Huybrechts

出品人:

頁數:309

译者:

出版時間:2010-1

價格:39.00元

裝幀:

isbn號碼:9787510004636

叢書系列:Universitext

圖書標籤:

數學
復幾何
complex_geometry
幾何
數學物理
入門
algebraic-geometry
物理&數學
復幾何
代數幾何
微分幾何
黎曼麯麵
復分析
上同調
解析幾何
代數拓撲
復流形
保角映射

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具體描述

《復幾何導論(英文版)》內容簡介：Complex geometry is a highly attractive branch of modern mathematics that has witnessed many years of active and successful research and that has recently 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 subject's 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.

著者簡介

圖書目錄

1 Local Theory 1
1.1 Holomorphic Functions of Several Variables 1
1.2 Complex and Hermitian Structures 25
1.3 Differential Forms 42
2 Complex Manifolds 51
2.1 Complex Manifolds: Definition and Examples 52
2.2 Holomorphic Vector Bundles 66
2.3 Divisors and Line Bundles 77
2.4 The Projective Space 91
2.5 Blow-ups 98
2.6 Differential Calculus on Complex Manifolds 104
3 Kahler Manifolds 113
3.1 Kahler Identities 114
3.2 Hodge Theory on Kahler Manifolds 125
3.3 Lefschetz Theorems 132
Appendix 145
3.A Formality of Compact Kahler Manifolds 145
3.B SUSY for Kahler Manifolds 155
3.C Hodge Structures 160
4 Vector Bundles 165
4.1 Hermitian Vector Bundles and Serre Duality 166
4.2 Connections 173
4.3 Curvature 182
4.4 Chern Classes 193
Appendix 206
4.A Levi-Civita Connection and Holonomy on Complex Manifolds . 206
4.B Hermite-Einstein and Kahler-Einstein Metrics 217
5 Applications of Cohomology 231
5.1 Hirzebruch-Riemann-Roch Theorem 231
5.2 Kodaira Vanishing Theorem and Applications 239
5.3 Kodaira Embedding Theorem 247
6 Deformations of Complex Structures 255
6.1 The Maurer-Cartan Equation 255
6.2 General Results 268
Appendix 275
6.A dGBV-Algebras 275
A Hodge Theory on Differentiate Manifolds 281
B Sheaf Cohomology 287
References 297
Index 303
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