We characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.
"Toric Fano varieties associated to building sets." Kyoto J. Math. 60 (1) 45 - 59, April 2020. https://doi.org/10.1215/21562261-2019-0034