Normality of 3-dimensional lattice polytopes

Shoetsu Ogata

doi:10.1016/j.endm.2013.07.014

Normality of 3-dimensional lattice polytopes

Shoetsu Ogata

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We construct examples of ample lattice polytope of dimension n≥ 3 such that the n- 2 times multiple of them are very ample but not normal. We also obtain two classes of normal 3-dimensional nonsingular lattice polytopes. One is a class of polytopes with relatively small internal polytopes. The other is that of polytopes which are the Minkowski sums with line segments.

Original language	English
Pages (from-to)	83-88
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	43
DOIs	https://doi.org/10.1016/j.endm.2013.07.014
Publication status	Published - 2013 Sep 9

Keywords

Lattice polytopes
Toric varieties

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1016/j.endm.2013.07.014

Cite this

@article{27820157d44b4afabad6a9aa92a189cf,

title = "Normality of 3-dimensional lattice polytopes",

abstract = "We construct examples of ample lattice polytope of dimension n≥ 3 such that the n- 2 times multiple of them are very ample but not normal. We also obtain two classes of normal 3-dimensional nonsingular lattice polytopes. One is a class of polytopes with relatively small internal polytopes. The other is that of polytopes which are the Minkowski sums with line segments.",

keywords = "Lattice polytopes, Toric varieties",

author = "Shoetsu Ogata",

year = "2013",

month = sep,

day = "9",

doi = "10.1016/j.endm.2013.07.014",

language = "English",

volume = "43",

pages = "83--88",

journal = "Electronic Notes in Discrete Mathematics",

issn = "1571-0653",

publisher = "Elsevier",

}

TY - JOUR

T1 - Normality of 3-dimensional lattice polytopes

AU - Ogata, Shoetsu

PY - 2013/9/9

Y1 - 2013/9/9

N2 - We construct examples of ample lattice polytope of dimension n≥ 3 such that the n- 2 times multiple of them are very ample but not normal. We also obtain two classes of normal 3-dimensional nonsingular lattice polytopes. One is a class of polytopes with relatively small internal polytopes. The other is that of polytopes which are the Minkowski sums with line segments.

AB - We construct examples of ample lattice polytope of dimension n≥ 3 such that the n- 2 times multiple of them are very ample but not normal. We also obtain two classes of normal 3-dimensional nonsingular lattice polytopes. One is a class of polytopes with relatively small internal polytopes. The other is that of polytopes which are the Minkowski sums with line segments.

KW - Lattice polytopes

KW - Toric varieties

UR - http://www.scopus.com/inward/record.url?scp=84883389461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883389461&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2013.07.014

DO - 10.1016/j.endm.2013.07.014

M3 - Article

AN - SCOPUS:84883389461

VL - 43

SP - 83

EP - 88

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -

Normality of 3-dimensional lattice polytopes

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this