
Introduction to Complex Manifolds
John M. Lee(Author)
American Mathematical Society (Publisher)
Published on 30. September 2024
Book
Paperback/Softback
361 pages
978-1-4704-7782-0 (ISBN)
Description
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.
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
ISBN-13
978-1-4704-7782-0 (9781470477820)
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Schweitzer Classification
Person
John M. Lee, University of Washington, Seattle, WA.
Content
The basics
Complex submanifolds
Holomorphic vector bundles
The Dolbeault complex
Sheaves
Sheaf cohomology
Connections
Hermitian and Kahler manifolds
Hodge theory
The Kodaira embedding theorem
Complex submanifolds
Holomorphic vector bundles
The Dolbeault complex
Sheaves
Sheaf cohomology
Connections
Hermitian and Kahler manifolds
Hodge theory
The Kodaira embedding theorem