Smooth Fano polytopes can not be inductively constructed
Øbro, Mikkel
Tohoku Math. J. (2), Tome 60 (2008) no. 1, p. 219-225 / Harvested from Project Euclid
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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.
Publié le : 2008-05-15
Classification:  52B20,  14M25 
@article{1215442872,
     author = {\O bro, Mikkel},
     title = {Smooth Fano polytopes can not be inductively constructed},
     journal = {Tohoku Math. J. (2)},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 219-225},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1215442872}
}

Øbro, Mikkel. Smooth Fano polytopes can not be inductively constructed. Tohoku Math. J. (2), Tome 60 (2008) no. 1, pp.  219-225. http://gdmltest.u-ga.fr/item/1215442872/