Speaker: Jorge Lauret - Universidad Nacional de Córdoba & CIEM
Date: Friday, 09/05/2025 - 14h:00 GMT-3 (Brasilia - Buenos Aires)
Abstract:
Starting from a flag manifold F=G/H (the only compact homogeneous manifolds which are Kähler), each of the countable many closed tori T in the center Z(H) of even codimension defines a torus bundle M=G/K over F with fibre A=Z(H)/T, where K=[H,H]xT. The different slopes of T in Z(H) may or may not have topological consequences on M. These so-called C-spaces M=G/K are precisely the compact homogeneous spaces admitting invariant complex structures, which are all given by one of the finitely many complex structures on F and any left-invariant complex structure on the torus A, i.e., any linear map J_a on the Lie algebra a of A whose square is -I. The freedom to choose J_a is overwhelming. In this talk, we will show that the existence of distinguished Hermitian metrics like Hermite-Einstein, balanced, SKT, CYT, Chern-Einstein, etc., can be very sensitive to such a choice.
Previous talks.