The reflexive dimension of a lattice polytope

被引：15
作者：
Haase, Christian [1 ]
Melnikov, Ilarion V.
机构：
[1] Free Univ Berlin, Dept Math & Comp Sci, D-14195 Berlin, Germany
[2] Univ Chicago, Enrico Fermi Inst, Particle Theory Grp, Chicago, IL 60637 USA
来源：
ANNALS OF COMBINATORICS | 2006年 / 10卷 / 02期
基金：
美国国家科学基金会;
关键词：
reflexive polytopes;
D O I：
10.1007/s00026-006-0283-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The reflexive dimension refldim (P) of a lattice polytope P is the minimal integer d so that P is the face of some d-dimensional reflexive polytope. We show that refldim (P) is finite for every P, and give bounds for refldim(kP) in terms of refldim (P) and k.
引用
收藏
页码：211 / 217
页数：7
相关论文
共 16 条
[1]  
Barvinok A., 2002, Graduate Studies in Mathematics, V54
[2]  
Batyrev V. V., 1994, J ALGEBRAIC GEOM, V3, P493
[3]  
Fulton W., 1993, ANN MATH STUD, V131
[4]  
HAASE C, CONT MATH, V374, pR11
[5]   DUAL POLYTOPES OF RATIONAL CONVEX POLYTOPES [J].
HIBI, T .
COMBINATORICA, 1992, 12 (02) :237-240
[6]   PALP: A package for analysing lattice polytopes with applications to toric geometry [J].
Kreuzer, M ;
Skarke, H .
COMPUTER PHYSICS COMMUNICATIONS, 2004, 157 (01) :87-106
[7]  
Kreuzer M., 1998, ADV THEOR MATH PHYS, V2, P847
[8]   Complete classification of reflexive polyhedra in four dimensions [J].
Kreuzer, Maximilian ;
Skarke, Harald .
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, 2000, 4 (06) :1209-1230
[9]   BOUNDS FOR LATTICE POLYTOPES CONTAINING A FIXED NUMBER OF INTERIOR POINTS IN A SUBLATTICE [J].
LAGARIAS, JC ;
ZIEGLER, GM .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1991, 43 (05) :1022-1035
[10]   SUMMING THE INSTANTONS - QUANTUM COHOMOLOGY AND MIRROR SYMMETRY IN TORIC VARIETIES [J].
MORRISON, DR ;
PLESSER, MR .
NUCLEAR PHYSICS B, 1995, 440 (1-2) :279-354
12