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On empty lattice simplices in dimension 4

2011
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Proceedings of the American Mathematical Society
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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 , . .

doi:10.1090/s0002-9939-2011-10859-1
fatcat:yn73jip2y5b3nfl2zljjihw5x4