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Geometric and Functional Analysis

, Volume 27, Issue 1, pp 78–129 | Cite as

Kähler–Einstein metrics on group compactifications

  • Thibaut Delcroix
Article

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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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Département de mathématiques et applicationsÉcole normale supérieureParis Cedex 05France

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