Buch, Englisch, 397 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1670 g
Buch, Englisch, 397 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1670 g
Reihe: Graduate Texts in Mathematics
ISBN: 978-0-387-95395-3
Verlag: Springer
This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
I Holomorphic Functions.- 1. Complex Geometry.- 2. Power Series.- 3. Complex Differentiable Functions.- 4. The Cauchy Integral.- 5. The Hartogs Figure.- 6. The Cauchy-Riemann Equations.- 7. Holomorphic Maps.- 8. Analytic Sets.- II Domains of Holomorphy.- 1. The Continuity Theorem.- 2. Plurisubharmonic Functions.- 3. Pseudoconvexity.- 4. Levi Convex Boundaries.- 5. Holomorphic Convexity.- 7. Examples and Applications.- 8. Riemann Domains over Cn.- 9. The Envelope of Holomorphy.- III Analytic Sets.- 1. The Algebra of Power Series.- 2. The Preparation Theorem.- 3. Prime Factorization.- 4. Branched Coverings.- 5. Irreducible Components.- 6. Regular and Singular Points.- IV Complex Manifolds.- 1. The Complex Structure.- 2. Complex Fiber Bundles.- 3. Cohomology.- 4. Meromorphie Functions and Divisors.- 5. Quotients and Submanifolds.- 6. Branched Riemann Domains.- 7. Modifications and Toric Closures.- V Stein Theory.- 1. Stein Manifolds.- 2. The Levi Form.- 3. Pseudoconvexity.- 4. Cuboids.- 5. Special Coverings.- 6. The Levi Problem.- VI Kahler Manifolds.- 1. Differential Forms.- 2. Dolbeault Theory.- 3. Kähler Metrics.- 4. The Inner Product.- 5. Hodge Decomposition.- 6. Hodge Manifolds.- 7. Applications.- VII Boundary Behavior.- 1. Strongly Pseudoconvex Manifolds.- 2. Subelliptic Estimates.- 3. Nebenhüllen.- 4. Boundary Behavior of Biholomorphic Maps.- References.- Index of Notation.
