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Issue Section:. You do not currently have access to this article. Download all figures. On successful completion of this course, students should be able to: CLO 1 grasp the notion of holomorphic line bundles, understand various ways for establishing the existence of global holomorphic sections of line bundles, and to relate them to the embedding of compact complex manifolds CLO 2 grasp the relationship between sheaf cohomology, de Rham cohomology and d-bar cohomology, and make use of the relationship to solve various existence problems by means of vanishing theorems on harmonic forms CLO 3 grasp the basics of complex differential geometry such as notions of connections and curvature on Kahler manifolds and on Hermitian holomorphic vector bundles, and be able to relate various notions of positivity of curvature and apply them to vanishing and embedding theorems CLO 4 identify the key elements in the theoretic foundation of various additional topics covered in the course and to make use of them in solving problems.
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Hodge Theory and Complex Algebraic Geometry I: Volume 1 by Claire Voisin
This course aims to present the foundation of the theory of complex manifolds and to introduce students to a variety of research topics, focusing on compact complex manifolds. Gunning and H. Rossi: Analytic functions of several complex variables. Prentice Hall Grauert and R.
Remmert: The theory of Stein spaces. Grundlagen der Mathematischen Wissenschaft , Springer-Verlag Rice Studies , pp. Helgason: Differential geometry and sywmetric spaces.
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Van Nostrand Reinhold Kodaira and J. Morrow: Complex manifolds.
Holt, Rinehart and Winston Kobayashi, K. Nomizu: Foundations of differential geometry. Wiley-Interscience vol. Symposia Math.
Milnor: Morse theory. Mori: Projective manifolds with ample tangent bundles. Narasimhan: Analysis on real and complex manifolds. Nachbin: Holomorphic functions, domains of holomorphy and local properties. North Holland Newlander and L.