Introduction to complex manifolds
著者
書誌事項
Introduction to complex manifolds
（Graduate studies in mathematics, 244）
American Mathematical Society, c2024
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注記
Includes bibliographical references (p. 343-346) and indexes
内容説明・目次
内容説明
Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds (mainly compact ones), and it tells a story. Starting from familiarity with smooth manifolds and Riemannian geometry, it gradually explains what is different about complex manifolds and develops most of the main tools for working with them, using the Kodaira embedding theorem as a motivating project throughout.
The approach and style will be familiar to readers of the author's previous graduate texts: new concepts are introduced gently, with as much intuition and motivation as possible, always relating new concepts to familiar old ones, with plenty of examples. The main prerequisite is familiarity with the basic results on topological, smooth, and Riemannian manifolds. The book is intended for graduate students and researchers in differential geometry, but it will also be appreciated by students of algebraic geometry who wish to understand the motivations, analogies, and analytic results that come from the world of differential geometry.
目次
The basics
Complex submanifolds
Holomorphic vector bundles
The Dolbeault complex
Sheaves
Sheaf cohomology
Connections
Hermitian and Kahler manifolds
Hodge theory
The Kodaira embedding theorem
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