Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
arXiv:1812.07218 · doi:10.1016/j.matpur.2020.12.002
Abstract
We give necessary and sufficient conditions for existence of solutions to a general system of complex Monge-Ampère equations on Fano horosymmetric manifolds. In particular, we get necessary and sufficient conditions for existence of coupled Kähler-Ricci solitons, Mabuchi metrics and twisted Kähler-Einstein metrics in terms of combinatorial data of the manifold.
arXiv commentaccepted version
References in corpus (8)
- K-Stability of Fano spherical varieties
- Kähler-Einstein metrics on group compactifications
- Mabuchi Solitons and Relative Ding Stability of Toric Fano Varieties
- Fano threefolds with infinite automorphism groups
- K{ä}hler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functional
- Coupled Kähler-Ricci solitons on toric Fano manifolds
- Mabuchi metrics and properness of the modified DING functional
- Relative Ding and -stability of toric Fano manifolds in low dimensions
Cited by in corpus (10)
- Basis divisors and balanced metrics
- Uniform K-stability of polarized spherical varieties
- The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds
- Ricci iteration for coupled Kähler-Einstein metrics
- Geometric quantization of coupled Kähler-Einstein metrics
- Examples of K-unstable Fano manifolds
- Residue formula for an obstruction to Coupled Kähler-Einstein metrics
- Deformation for coupled Kähler-Einstein metrics
- Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
- Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one