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Article Dans Une Revue Compositio Mathematica Année : 2018

Geometry and topology of the space of Kähler metrics on singular varieties

Résumé

Let Y be a compact Kähler normal space and α ∈ H1,1BC (Y) a Kähler class. We study metric properties of the space Hα of Kähler metrics in α using Mabuchi geodesics. We extend several results by 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 Q-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.
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Dates et versions

hal-01947248 , version 1 (06-12-2018)

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Eleonora Di Nezza, Vincent Guedj. Geometry and topology of the space of Kähler metrics on singular varieties. Compositio Mathematica, 2018, 154 (8), pp.1293-1632. ⟨10.1112/S0010437X18007170⟩. ⟨hal-01947248⟩
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