Generalized Kähler Einstein metrics and uniform stability for toric Fano manifolds. (English) Zbl 1439.53047

Summary: We give a complete criterion for the existence of generalized Kähler Einstein metrics on toric Fano manifolds from view points of a uniform stability in a sense of GIT and the properness of a functional on the space of Kähler metrics.


53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
58E11 Critical metrics
14J45 Fano varieties
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