DOCUMENTA MATHEMATICA, Vol. 7 (2002), 463-480

Winfried Bruns and Joseph Gubeladze

Unimodular Covers of Multiples of Polytopes

Let $P$ be a $d$-dimensional lattice polytope. We show that there exists a natural number $c_d$, only depending on $d$, such that the multiples $cP$ have a unimodular cover for every natural number $c\ge c_d$. Actually, an explicit upper bound for $c_d$ is provided, together with an analogous result for unimodular covers of rational cones.

2000 Mathematics Subject Classification: Primary 52B20, 52C07, Secondary 11H06

Keywords and Phrases: lattice polytope, rational cone, unimodular covering

Full text: dvi.gz 35 k, dvi 97 k, ps.gz 724 k, pdf 215 k.