Smooth Fano polytopes arising from finite directed graphs

Abstract

In this paper, we consider terminal reflexive polytopes arising from finite directed graphs and study the problem of deciding which directed graphs yield smooth Fano polytopes (SFPs). We show that any centrally symmetric or pseudosymmetric SFPs can be obtained from directed graphs. Moreover, by using directed graphs, we provide new examples of SFPs whose corresponding varieties admit Kähler–Einstein metrics.