Orbifold Kähler-Einstein metrics on projective toric varieties

Abstract

In this short note, we investigate the existence of orbifold Kähler-Einstein metrics on toric varieties. In particular, we show that every $\mathbb{Q}$-factorial normal projective toric variety allows an orbifold Kähler-Einstein metric. Moreover, we characterize the K-stability of $\mathbb{Q}$-factorial toric pairs of Picard number one in terms of the log Cox ring and the universal orbifold cover.

5 pages, new version: obtained a more general main statement building on results of Blum/Liu as well as an alternative convex geometric proof for these results. Comments are of course still very welcome