## Smooth Fano polytopes can not be inductively constructed

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

### Standard

Smooth Fano polytopes can not be inductively constructed. / Øbro, Mikkel.

I: Tohoku Mathematical Journal, Bind 60, Nr. 2, 2008, s. 219-225.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

### Harvard

Øbro, M 2008, 'Smooth Fano polytopes can not be inductively constructed', Tohoku Mathematical Journal, bind 60, nr. 2, s. 219-225. https://doi.org/10.2748/tmj/1215442872

### APA

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

### MLA

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

### Author

Øbro, Mikkel. / Smooth Fano polytopes can not be inductively constructed. I: Tohoku Mathematical Journal. 2008 ; Bind 60, Nr. 2. s. 219-225.

### Bibtex

@article{95469010de5c11dd9b3b000ea68e967b,
title = "Smooth Fano polytopes can not be inductively constructed",
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.",
author = "Mikkel {\O}bro",
year = "2008",
doi = "10.2748/tmj/1215442872",
language = "English",
volume = "60",
pages = "219--225",
journal = "Tohoku Mathematical Journal",
issn = "0040-8735",
publisher = "Tohoku Daigaku Suugaku Kyoshitsu",
number = "2",

}

### RIS

TY - JOUR

T1 - Smooth Fano polytopes can not be inductively constructed

AU - Øbro, Mikkel

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

U2 - 10.2748/tmj/1215442872

DO - 10.2748/tmj/1215442872

M3 - Journal article

VL - 60

SP - 219

EP - 225

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

SN - 0040-8735

IS - 2

ER -