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Kähler–Einstein metrics on group compactifications

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Abstract

We obtain a necessary and sufficient condition of existence of a Kähler–Einstein metric on a G × G-equivariant Fano compactification of a complex connected reductive group G in terms of the associated polytope. This condition is not equivalent to the vanishing of the Futaki invariant. The proof relies on the continuity method and its translation into a real Monge–Ampère equation, using the invariance under the action of a maximal compact subgroup K × K.

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  1. Département de mathématiques et applications, École normale supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Thibaut Delcroix

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Delcroix, T. Kähler–Einstein metrics on group compactifications. Geom. Funct. Anal. 27, 78–129 (2017). https://doi.org/10.1007/s00039-017-0394-y

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