Basic materials on compact Kaehler manifolds will be explained.
To understand special properties on cohomology groups on compact Kahler manifolds, as well as their proofs.
Kahler metric, Kahler manifold, Hodge decomposition, Kahelr identity, Lefschetz decomposition, primitive cohomology, Hodge index theorem, divisors and line bundles
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
|Course schedule||Required learning|
|Class 1||Kahler manifolds and examples||Details will be provided during each class session|
|Class 2||Hodge decomposition|
|Class 3||Kahler identity|
|Class 4||primitive cohomology|
|Class 5||Lefschetz decomposition|
|Class 6||index formula|
|Class 7||divisors and line bundles|
|Class 8||Picard groups and Chern classes|
P. Griffiths, J. Harris, "Principles of Algebraic Geometry", Wiley-Interscience
R.O.Wells, Differential analysis on complex manifolds, Springer GTM 65