K\"ahler-Einstein metrics on group compactifications
Differential Geometry
2020-09-16 v2 Algebraic Geometry
Abstract
We obtain a necessary and sufficient condition of existence of a K{\"a}hler-Einstein metric on a -equivariant Fano compactification of a complex connected reductive group 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-Amp{\`e}re equation, using the invariance under the action of a maximal compact subgroup .
Cite
@article{arxiv.1510.07384,
title = {K\"ahler-Einstein metrics on group compactifications},
author = {Thibaut Delcroix},
journal= {arXiv preprint arXiv:1510.07384},
year = {2020}
}