Toric Fano varieties associated to graph cubeahedra

TL;DR

This paper characterizes when the toric varieties derived from graph cubeahedra are Fano or weak Fano, based on properties of the underlying finite simple graph.

Contribution

It provides a complete combinatorial criterion linking graph properties to the Fano and weak Fano conditions of associated toric varieties.

Findings

Criteria for Fano and weak Fano conditions in terms of graph properties

Necessary and sufficient conditions for nonsingular projective toric varieties

Connection between graph structure and algebraic geometric properties

Abstract

We give a necessary and sufficient condition for the nonsingular projective toric variety associated to the graph cubeahedron of a finite simple graph to be Fano or weak Fano in terms of the graph.