Resumen de Rigid Gorenstein toric Fano varieties arising from directed graphs

Selvi Kara, Irem Portakal, Akiyoshi Tsuchiya

• A directed edge polytope AG is a lattice polytope arising from root system An and a finite directed graph G. If every directed edge of G belongs to a directed cycle in G, then AG is terminal and reflexive, that is, one can associate this polytope to a Gorenstein toric Fano variety XG with terminal singularities. It is shown by Totaro that a toric Fano variety which is smooth in codimension 2 and Q-factorial in codimension 3 is rigid. In the present paper, we classify all directed graphs G such that XG is a toric Fano variety which is smooth in codimension 2 and Q-factorial in codimension 3.