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On empty lattice simplices in dimension 4


Authors: Margherita Barile, Dominique Bernardi, Alexander Borisov and Jean-Michel Kantor
Journal: Proc. Amer. Math. Soc. 139 (2011), 4247-4253
MSC (2010): Primary 14B05; Secondary 14M25, 52B20
DOI: https://doi.org/10.1090/S0002-9939-2011-10859-1
Published electronically: April 28, 2011
MathSciNet review: 2823070
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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.


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Additional Information

Margherita Barile
Affiliation: Dipartimento di Matematica, Università di Bari “Aldo Moro”, Via E. Orabona 4, 70125 Bari, Italy
Email: barile@dm.uniba.it

Dominique Bernardi
Affiliation: Université Pierre et Marie Curie, Institut Mathématique de Jussieu, 175 Rue du Chevaleret, F-75013, Paris, France
Email: bernardi@math.jussieu.fr

Alexander Borisov
Affiliation: Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: borisov@pitt.edu

Jean-Michel Kantor
Affiliation: Université Paris Diderot, Institut Mathématique de Jussieu, 175 Rue du Chevaleret, F-75013, Paris, France
Email: kantor@math.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9939-2011-10859-1
Keywords: Lattice polytopes, terminal singularities, width
Received by editor(s): May 6, 2010
Received by editor(s) in revised form: October 22, 2010
Published electronically: April 28, 2011
Additional Notes: The research of the first author has been co-financed by the Italian Ministry of Education, University and Research (PRIN “Algebra Commutativa, Combinatoria e Computazionale”).
The research of the third author has been supported by NSA, grant H98230-08-1-0129
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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