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2008 Smooth Fano polytopes can not be inductively constructed
Mikkel Øbro
Tohoku Math. J. (2) 60(2): 219-225 (2008). DOI: 10.2748/tmj/1215442872

Abstract

We examine a concrete smooth Fano 5-polytope $P$ with 8 vertices with the following properties: There does not exist a smooth Fano 5-polytope $Q$ with 7 vertices such that $P$ contains $Q$, and there does not exist a smooth Fano 5-polytope $R$ with 9 vertices such that $R$ contains $P$. As the polytope $P$ is not pseudo-symmetric, it is a counter example to a conjecture proposed by Sato.

Citation

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Mikkel Øbro. "Smooth Fano polytopes can not be inductively constructed." Tohoku Math. J. (2) 60 (2) 219 - 225, 2008. https://doi.org/10.2748/tmj/1215442872

Information

Published: 2008
First available in Project Euclid: 7 July 2008

zbMATH: 1154.52010
MathSciNet: MR2428861
Digital Object Identifier: 10.2748/tmj/1215442872

Subjects:
Primary: 52B20
Secondary: 14M25

Rights: Copyright © 2008 Tohoku University

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Vol.60 • No. 2 • 2008
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