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【MSRI】Complex Geometry 简简单单的复几何
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https://www.msri.org/people/15110 Prerequisites: - Basics of manifolds, tensor fields, differential forms, etc. Warner, Foundations of Differentiable Manifolds and Lie Groups, Chapters 1, 2, 4, 6, contains all we need and much more. - Basic complex analysis as in Stein & Shakarchi, Complex Analysis, Chapters 1, 2, 3, 8. Reading: - Huybrechts, Complex Geometry, is an excellent basic textbook with exercises. - Lecture notes by Joel Fine: http://homepages.ulb.ac.be/∼joelfine/papers.html#survey. - Complex Monge-Ampere: http://gamma.im.uj.edu.pl/∼blocki/publ/ln/tln.pdf. - For the end of Week 2: http://arxiv.org/pdf/0803.0985.pdf, Section 5. Week 1: Introduction to Complex Geometry Holomorphic Functions and Complex Calculus Complex Manifolds Holomorphic Line Bundles Pseudoconvexity and Pseudoconcavity The Kodaira Embedding Theorem Week 2: Topics in Kahler-Einstein Manifolds Kahler Manifolds Ricci Curvature and the Complex Monge-Ampere Equation Examples of Ricci-flat Spaces Basic Estimates for the Complex Monge-Ampere Equation The Mukai-Umemura Manifold
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