Divisors on Projective Hibi Varieties

TL;DR

This paper computes the divisor class group and Picard group of projective Hibi varieties, which are toric varieties linked to order polytopes, using combinatorial properties of posets.

Contribution

It provides a combinatorial description of divisor and Picard groups for projective Hibi varieties, connecting algebraic geometry with poset theory.

Findings

Explicit formulas for divisor class group and Picard group

Description depends solely on poset combinatorics

Applicable to toric varieties from order polytopes

Abstract

We compute the divisor class group and the Picard group of projective varieties with Hibi rings as homogeneous coordinate rings. These varieties are precisely the toric varieties associated to order polytopes. We use tools from the theory of toric varieties to get a description of the two groups which only depends on combinatorial properties of the underlying poset.