Toric rings of (0,1)-polytopes with small rank

Abstract

The rank of a d-dimensional polytope P is defined by $F-(d+1)$, where F denotes the number of facets of P. In this paper, we focus on the toric rings of $(0,1)$-polytopes with small rank. We study their normality, the torsion-freeness of their divisor class groups, and the classification of their isomorphism classes.