- Andrei Moroianu, "Lectures on Kähler Geometry", LMS
- Claire Voisin, "Hodge Theory and Complex Algebraic Geometry, I", Cambridge
- Jean-Pierre Demailly, "Complex Analytic and Differential Geometry", https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf
- Daniel Huybrechts, "Complex Geometry", Springer
- Werner Ballmann, "Lectures on Kähler Manifolds", EMS
Learning Objectives
To learn notions, tools, methodology aimed to investigation and research in symplectic, Riemannian, complex, Kählerian geometry, and to strengthen abilities in processing and presentation.
Prerequisites
Basics in Differential Geometry and Riemannian Geometry.
Teaching Methods
Lessons and exercises, seminars.
Further information
For further information, contact the teachers.
Type of Assessment
Oral exam.
Course program
- Complex geometry: holomorphic functions of several variables; differential geometry of almost-complex manifolds and complex manifolds; integrability of almost-complex structures; examples; Riemann Uniformization Theorem, and classification of compact complex surfaces; sheaves and cohomology.
- Symplectic geometry: differential geometry of symplectic manifolds.
- Riemannian and Hermitian geometry: Hermitian metrics; connections and curvature of Hermitian metrics; elliptic Hodge theory.
- Kählerian geometry: Kähler structures; projective algebraic manifolds and Kodaira embedding theorem; Hodge theory for Kähler manifolds; curvature of Kähler metrics; special Kähler metrics; non-linear problems in Hermitian and Kähleriane geometry.