Graded Cohen-Macaulay domains and lattice polytopes with short $h$-vector

Abstract

Let P be a lattice polytope with $h^{\ast }$-vector $(1,h_1^{\ast },h_2^{\ast })$. In this note we show that if $h_2^{\ast }\le h_1^{\ast }$, then $P$ is IDP. More generally, we show the corresponding statements for semi-standard graded Cohen-Macaulay domains over algebraically closed fields.

8 Pages