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be a compact Kähler normal space and let
be a Kähler class. We study metric properties of the space
of Kähler metrics in
using Mabuchi geodesics. We extend several results of Calabi, Chen, and Darvas, previously established when the underlying space is smooth. As an application, we analytically characterize the existence of Kähler–Einstein metrics on
-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.
Nous montrons que l'entropie topologique des applications méromorphes n'est pas un invariant biméromorphe. Cela fournit un contre-exemple à une conjecture de Friedland. Nous proposons une version raffinée de cette conjecture.
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