Smooth Fano polytopes arising from finite directed graphs

Abstract

In this paper, we consider terminal reflexive polytopes arising from finite directed graphs and study the problem of deciding which directed graphs yield smooth Fano polytopes. We show that any centrally symmetric or pseudo-symmetric smooth Fano polytopes can be obtained from directed graphs. Moreover, by using directed graphs, we provide new examples of smooth Fano polytopes whose corresponding varieties admit Kähler--Einstein metrics.

13 pages, 4 figures

References in corpus (3)

• Canonical toric Fano threefolds
• An algorithm for the classification of smooth Fano polytopes
• Roots of Ehrhart polynomials arising from graphs

Cited by in corpus (10)

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• Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part
• The $h^{\ast }$-polynomials of locally anti-blocking lattice polytopes and their $\gamma$-positivity
• Reverse lexicographic squarefree initial ideals and Gorenstein Fano polytopes
• On the gamma-vector of symmetric edge polytopes
• Likelihood Geometry of Reflexive Polytopes
• Facets of Random Symmetric Edge Polytopes, Degree Sequences, and Clustering
• Toric Fano varieties associated to building sets
• Notes on toric Fano varieties associated to building sets
• Rigid Gorenstein toric Fano varieties arising from directed graphs