On empty lattice simplices in dimension 4

Margherita Barile; Dominique Bernardi; Alexander Borisov; Jean Michel Kantor

doi:10.1090/S0002-9939-2011-10859-1

On empty lattice simplices in dimension 4

Margherita Barile
, Dominique Bernardi
, Alexander Borisov
, Jean Michel Kantor

Mathematics and Statistics

Binghamton University

University of Bari
Sorbonne Université
Université Paris Cité

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

16 Scopus citations

Abstract

We give an almost complete classification of empty lattice simplices in dimension 4 using the conjectural results of Mori-Morrison-Morrison, which were later proved by Sankaran and Bober. In particular, all of these simplices correspond to cyclic quotient singularities, and all but finitely many of them have width bounded by 2.

Original language	English
Pages (from-to)	4247-4253
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9939-2011-10859-1
State	Published - Dec 2011

Keywords

Lattice polytopes
Terminal singularities
Width

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10.1090/S0002-9939-2011-10859-1

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title = "On empty lattice simplices in dimension 4",

abstract = "We give an almost complete classification of empty lattice simplices in dimension 4 using the conjectural results of Mori-Morrison-Morrison, which were later proved by Sankaran and Bober. In particular, all of these simplices correspond to cyclic quotient singularities, and all but finitely many of them have width bounded by 2.",

keywords = "Lattice polytopes, Terminal singularities, Width",

author = "Margherita Barile and Dominique Bernardi and Alexander Borisov and Kantor, \{Jean Michel\}",

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doi = "10.1090/S0002-9939-2011-10859-1",

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T1 - On empty lattice simplices in dimension 4

AU - Barile, Margherita

AU - Bernardi, Dominique

AU - Borisov, Alexander

AU - Kantor, Jean Michel

PY - 2011/12

Y1 - 2011/12

N2 - We give an almost complete classification of empty lattice simplices in dimension 4 using the conjectural results of Mori-Morrison-Morrison, which were later proved by Sankaran and Bober. In particular, all of these simplices correspond to cyclic quotient singularities, and all but finitely many of them have width bounded by 2.

AB - We give an almost complete classification of empty lattice simplices in dimension 4 using the conjectural results of Mori-Morrison-Morrison, which were later proved by Sankaran and Bober. In particular, all of these simplices correspond to cyclic quotient singularities, and all but finitely many of them have width bounded by 2.

KW - Lattice polytopes

KW - Terminal singularities

KW - Width

UR - https://www.scopus.com/pages/publications/80051966421

U2 - 10.1090/S0002-9939-2011-10859-1

DO - 10.1090/S0002-9939-2011-10859-1

M3 - Article

SN - 0002-9939

VL - 139

SP - 4247

EP - 4253

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -

On empty lattice simplices in dimension 4

Abstract

Keywords

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