Toric Fano varieties associated to building sets

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.