Proof of a Conjecture of Batyrev and Juny on Gorenstein Polytopes

Abstract

AbstractA d-dimensional lattice polytope P is Gorenstein if it has a multiple rP that is a reflexive polytope up to translation by a lattice vector. The difference $$d+1-r$$ d + 1 - r is called the degree of P. We show that a Gorenstein polytope is a lattice pyramid if its dimension is at least three times its degree. This was previously conjectured by Batyrev and Juny. We also present a refined conjecture and prove it for IDP Gorenstein polytopes.