On the Width of Lattice-free Simplices

Compositio Mathematica

Volumn 118, Issue 3, 1999, Pages 235-241

  Kantor, Jean Michel ^a  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

Lattice; Lattice free (empty) polytopes; Polytopes; Simplices; Width

Indexed keywords

EID: 0042138257     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1001164317215     Document Type: Article

References (15)

1. Banaszczyk, W., Litvak, A. E., Pajor, A. and Szarek, S. J.: The Flatness Theorem for Non-symmetric Convex Bodies via the Local Theory of Banach Spaces (to appear).
2. Brion, M.: Points entiers dans les polytopes convexes, expose No. 780, Séminaire Bourbaki, mars 1994.
3. 21 whose 27 vertices correspond to the lines on the generic cubic surface, Amer. J. Math. 62 (1940), 457-486.
4. Dais, D.: Enumerative combinatorics of invariants of certain complex threefolds with trivial canonical bundle, Dissertation, Bonn, 1994.
5. Euler, L.: Introduction in Analysis Infinitorum, Vol. 1, Ch. 16 (1748), 253-257.
6. Frumkin, H.: Description of Elementary Three-dimensional Polyhedra, Conference on statistical and discrete analysis, Alma Ata, 1981 (Russian).
7. Kantor, J.M.: Triangulations of integral polytopes and Ehrhart polynomials, Beiträge Algebra Geom. 39(1) (1998), 205-218.
8. Kannan, R. and Lovasz, L.: Covering minima and lattice-point free convex bodies, Ann. of Math. 128 (1988), 577-602.
9. Mori, K., Morrison, D. and Morrison, I.: On four-dimensional terminal quotient singularities, Math. Comp. 51(184) (1988), 769-786.
10. Morrison, D. and Stevens, G.: Terminal quotient singularities in dimension three and four, Proc. Amer. Math. Soc. 90(1) (1984), 15-20.
11. Oda, T.: Convex Bodies and Algebraic Geometry, Ergeb. Math. Grenzgeb. (3), Springer-Verlag, 1988.
12. Scarf, H. E.: Integral polyhedra in three space, Math. Oper. Res. 10 (1985), 403-438.
13. Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press, 1971.
14. Wessels.: Die Sätze von White, Diplomarbeït, Bochum, 1989.
15. White, G. K.: Lattice tetrahedra, Canad. J. Math. 16 (1961), 389-396.