On the maximal dual volume of a lattice polytope with one interior point

Abstract

It is well known that the volume of a canonical Fano lattice polytope P (i.e a lattice polytope with one interior lattice point) of some fixed dimension is bounded. A sharp bound has been conjectured, but never been proved. In a joint work with A. Kasprzyk and B. Nill we prove that such sharp bound is valid (and sharp) when the volume of the dual P is considered. As a corollary we have a sharp bound for the volume of reflexive polytopes.