On empty lattice simplices in dimension 4

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

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

On empty lattice simplices in dimension 4
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by Margherita Barile, Dominique Bernardi, Alexander Borisov and Jean-Michel Kantor

Proc. Amer. Math. Soc. 139 (2011), 4247-4253

DOI: https://doi.org/10.1090/S0002-9939-2011-10859-1

Published electronically: April 28, 2011

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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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