Toric Fano varieties associated to building sets
Yusuke Suyama

TL;DR
This paper characterizes building sets that produce Fano toric varieties and shows they originate from smooth Fano polytopes linked to finite directed graphs.
Contribution
It provides a complete characterization of building sets leading to Fano toric varieties and connects these to smooth Fano polytopes from directed graphs.
Findings
Characterization of building sets for Fano toric varieties
All such varieties derive from smooth Fano polytopes
Connection established between toric varieties and directed graphs
Abstract
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.
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