Torsionfreeness for divisor class groups of toric rings of integral polytopes

Abstract

In the present paper, we give some sufficient conditions for Cl(k[P]) to be torsionfree, where Cl(k[P]) denote the divisor class group of the toric ring k[P] of an integral polytope P. We prove that Cl(k[P]) is torsionfree if P is compressed, and Cl(k[P]) is torsionfree if P is a (0,1)-polytope which has at most dim⁡P+2 facets. Moreover, we characterize the toric rings of (0,1)-polytopes in the case Cl(k[P])≅Z.