Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 55, Number 3 (2015), 579-592.
Smooth Fano polytopes arising from finite directed graphs
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.
Kyoto J. Math., Volume 55, Number 3 (2015), 579-592.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 05C20: Directed graphs (digraphs), tournaments
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