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

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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.",

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author = "Shoetsu Ogata",

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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

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DO - 10.1016/j.endm.2013.07.014

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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

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