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arXiv · 1103.2202

Smooth Fano polytopes arising from finite directed graphs

Akihiro Higashitani
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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.

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Akihiro Higashitani. 2014-06-30. Smooth Fano polytopes arising from finite directed graphs. https://doi.org/10.1215/21562261-3089073

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