Kyoto Journal of Mathematics

Smooth Fano polytopes arising from finite directed graphs

Akihiro Higashitani

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 (SFPs). We show that any centrally symmetric or pseudosymmetric SFPs can be obtained from directed graphs. Moreover, by using directed graphs, we provide new examples of SFPs whose corresponding varieties admit Kähler–Einstein metrics.

Article information

Source
Kyoto J. Math., Volume 55, Number 3 (2015), 579-592.

Dates
Received: 22 July 2013
Revised: 24 April 2014
Accepted: 2 July 2014
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1441824037

Digital Object Identifier
doi:10.1215/21562261-3089073

Mathematical Reviews number (MathSciNet)
MR3395979

Zentralblatt MATH identifier
1333.14047

Citation

Higashitani, Akihiro. Smooth Fano polytopes arising from finite directed graphs. Kyoto J. Math. 55 (2015), no. 3, 579--592. doi:10.1215/21562261-3089073. https://projecteuclid.org/euclid.kjm/1441824037

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