Department of Mathematics

Verallgemeinerte komplexe Geometrie

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Wahlfächer Analysis, Algebra und Zahlentheorie, Geometrie, mathematische Physik
Dozenten Giovanni Felder, Chenchang Zhu, Carlo A. Rossi
Ort HG D3.1
Zeit Di 10.15-12.00
Beginnt am Di 4. April 2006
Vorbesprechung Di 4. April 2006, 10.15, Hermann Weyl-Zimmer HG G43
Kontakt Chenchang Zhu
Voraussetzungen Differenzialgeometrie
Beschreibung The notion of generalized geometry was introduced by N. Hitchin to give a geometrical setting for certain computations in string theory.
The basic idea is to replace the tangent bundle T by the direct sum T+T* of the tangent bundle and the cotangent bundle. Generalized complex structures interpolate between symplectic and complex structures. They are endomorphisms of T+T* squaring to -1 and obeying an integrability condition.
In this seminar we first discuss basic notions of symplectic, complex and Kaehler differential geometry and then turn to generalized complex geometry. Application to complex geometry and possibly physics will also be presented.
Literatur Lectures on Symplectic Geometry by Ana Cannas Da Silva,
Principles of Algebraic Geometry by Griffiths and Harris (Chapter 0),
New proof for the existence of locally complete families of complex structures, by M. Kuranishi appeared
in Proc. Conf. Complex Analysis (Minneapolis, 1964), pages 142–154
Generalized Complex Geometry, by Marco Gualtieri, available online at
Weitere Informationen Syllabus and Lecture Notes

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