MAGIC044: Complex Differential Geometry

Course details

Semester

Autumn 2009
Monday, October 5th to Friday, December 11th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
0

Description

Literature
S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry", vol. II, John Wiley & Sons
A. Moroianu, "Lectures on Kähler Geometry", CUP
C. Voisin, "Hodge theory and complex algebraic geometry", vol. I, CUP
P. Griffiths and J. Harris, "Principles of Algebraic Geometry", John Wiley & Sons (chapter 0 only)

Additional reading material
K. Fritzsche and H. Grauert, "From Holomorphic Functions to Complex Manifolds", Springer
D. Huybrechts, "Complex Geometry, Springer
W. Ballman, "Lectures on Kähler manifolds", EMS
R.O. Wells, "Differential analysis on complex manifolds", Springer

Prerequisites

Familiarity with basic notions of topological and differentiable manifolds, especially tensors and differential forms.
Knowledge of such Riemannian concepts as the Levi-Civita connection and curvature will be helpful, but not essential.

Syllabus

1. Complex and almost complex manifolds
2. Holomorphic forms and vector fields
3. Complex and holomorphic vector bundles
4. Hermitian bundles, metric connections, curvature
5. Chern classes
6. Hermitian and Kähler metrics
7. Dolbeaut theory and the Hodge theorem
8. Curvature of Kähler manifolds; holomorphic sectional curvature
9. Ricci curvature of Kähler manifolds
10. Kähler-Einstein manifolds
11. Calabi-Yau manifolds

Lecturer

  • RB

    Prof Roger Bielawski

    University
    University of Leeds

Bibliography

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Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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