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Technical University of Munich

Reading Seminar

Complex Geometry

Mentor: Prof. Dr. Liedtke, Organizer: Gebhard Martin

 

Time and Place

Mondays 12:30 - 14:00 in 02.12.20

Contents

Coming from the algebraic point of view, we want to see the advantages of doing geometry with respect to the analytic topology over the complex numbers.

The first goal of the seminar is to learn from scratch the techniques used in Complex Geometry, such as Dolbeault Cohomology, Kähler Metrics, Hodge Theory, Chern Classes etc.

The second goal is to use the additional insight we get from doing Complex Geometry to gain a better understanding of the geometric concepts in the algebraic setting. This is reasonable, since many seemingly abstract ideas used in Algebraic Geometry stem from the more intuitive notions over the complex numbers.

In the second semester of this reading course, we follow the very geometric ideas of "Principles of Algebraic Geometry" to learn some of the deeper aspects of the theory of complex curves and surfaces.

Literature

P. Griffiths, J. Harris: Principles of Algebraic Geometry
D. Huybrechts: Complex Geometry

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