Let $G$ be a complex semisimple group. In this note, we give a method to classify $\mathbb Q$-Fano compactifications of $G$. We will prove that there are only finitely many $\mathbb Q$-Fano $G$-compactifications that admit (singular) Kähler–Einstein metrics. As an application, this improves a former result in [ 19].

中文翻译：

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具有 Kähler-Einstein 度量的半单群 ℚ-Fano 紧化的有限性

令$G$ 为复半单群。在这篇笔记中，我们给出了一种对 $G$ 的 $\mathbb Q$-Fano 紧化进行分类的方法。我们将证明只有有限多个 $\mathbb Q$-Fano $G$-compactifications 承认（单数）Kähler-Einstein 度量。作为一个应用程序，这改进了 [19] 中的先前结果。