HOME > Table of Contents and Abstracts > Vol. 60, No. 2
Tohoku Mathematical Journal
SECOND SERIES VOL. 60, NO. 2
|Tohoku Math. J.|
60 (2008), 219-225
SMOOTH FANO POLYTOPES CAN NOT BE INDUCTIVELY CONSTRUCTED
(Received March 26, 2007, revised September 10, 2007)
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.
2000 Mathematics Subject Classification.
Primary 52B20; Secondary 14M25.
Key words and phrases.
Smooth Toric Fano varieties.
To the top of this page
Back to the Contents