Unimodular covers of multiples of polytopes

Abstract

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.