28 aug 2018 - 4 sep 2018
FaMAF, Universidad Nacional de Córdoba (Argentina)
K\"ahler geometry provides analytic techniques to extend results from the algebraic to the transcendental setting. Non-K\"ahler geometry is then the attempt to perform a separate analysis of the complex and symplectic contributions. The very ultimate aim is a tentative classification of compact complex manifolds, by means of cohomological invariants and canonical Hermitian metrics.
First lecture
Cohomological invariants of complex manifolds.
- Complex and almost-complex manifolds.
- The double complex of forms on a complex manifold.
- Cohomologies of complex manifolds: sheaves and elliptic Hodge theory.
- Relation between cohomologies, and the $\partial\overline\partial$-Lemma.
Second lecture
Special Hermitian metrics on complex manifolds.
- Hermitian metrics on complex manifolds.
- Chern connection of Hermitian metrics.
- K\"ahler manifolds.
- Hodge theory for K\"ahler manifolds and algebraic projective manifolds.
Third lecture
Further topics.
- Cohomologies of solvmanifolds.
- Rational homotopy theory of compact K\"ahler manifolds.
- LCK geometry as "equivariant (homothetic) K\"ahler geometry".
Organizers: Adrian Andrada.
Courses:
28 Aug 2018: D. Angella: Curso: An invitation to complex non-Kähler geometry. I. Aula 12, FaMAF, Universidad Nacional de Córdoba
3 Sep 2018: D. Angella: Curso: An invitation to complex non-Kähler geometry. II. Aula 12, FaMAF, Universidad Nacional de Córdoba
4 Sep 2018: D. Angella: Curso: An invitation to complex non-Kähler geometry. III. Aula 12, FaMAF, Universidad Nacional de Córdoba
Speakers: Daniele Angella.