Abstract
AbstractA directed edge polytope $${\mathcal {A}}_G$$
A
G
is a lattice polytope arising from root system $$A_n$$
A
n
and a finite directed graph G. If every directed edge of G belongs to a directed cycle in G, then $${\mathcal {A}}_G$$
A
G
is terminal and reflexive, that is, one can associate this polytope to a Gorenstein toric Fano variety $$X_G$$
X
G
with terminal singularities. It is shown by Totaro that a toric Fano variety which is smooth in codimension 2 and $${\mathbb {Q}}$$
Q
-factorial in codimension 3 is rigid. In the present paper, we classify all directed graphs G such that $$X_G$$
X
G
is a toric Fano variety which is smooth in codimension 2 and $${\mathbb {Q}}$$
Q
-factorial in codimension 3.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics
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