On empty lattice simplices in dimension 4

Margherita Barile, Dominique Bernardi, Alexander Borisov, Jean-Michel Kantor
2011 Proceedings of the American Mathematical Society  
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. Let e 1 , . . . , e d be the canonical basis of R d . Then the quotient group G = D/D is isomorphic to the direct sum d i=1 Z/m i Z for some positive integers m 1 , . .
more » ... integers m 1 , . . . , m d . According to the construction described, e.g., in [5], Chapter 2, the affine toric variety U σ associated with σ can be viewed as the (Q-factorial toric) quotient singularity C d /G, where the action of G on C d is defined as follows: for all r 1 . . . , r d ∈ Z and all (
doi:10.1090/s0002-9939-2011-10859-1 fatcat:yn73jip2y5b3nfl2zljjihw5x4