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 ‐factorial normal projective toric variety allows an orbifold Kähler–Einstein metric. Moreover, we characterize ‐stability of ‐factorial toric pairs of Picard number one in terms of the log Cox ring and the universal orbifold cover.