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

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