Lattice polytopes with a given $h^{\ast }$-polynomial

Victor Batyrev

Let $\Delta \subset {\mathbb{R}}^n$ be an $n$-dimensional lattice polytope. It is well-known that $h_{\Delta }^{\ast }(t):=(1-t{)}^{n+1}{\sum }_{k\ge 0}|k\Delta \cap {\mathbb{Z}}^n|t^k$ is a polynomial of degree $d\le n$…