Tohoku Mathematical Journal
2008
June
SECOND SERIES VOL. 60, NO. 2

Tohoku Math. J.
60 (2008), 219-225

Title SMOOTH FANO POLYTOPES CAN NOT BE INDUCTIVELY CONSTRUCTED

Author Mikkel Øbro

(Received March 26, 2007, revised September 10, 2007)
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.

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