On the depth of simplicial affine semigroup rings

TL;DR

This paper explores the depth properties of affine semigroup rings, offering new characterizations especially for depth two in low dimensions, linked to Apery sets.

Contribution

It introduces an original characterization of depth two in three and four dimensions related to maximal elements in Apery sets.

Findings

Characterization of depth two in low-dimensional affine semigroup rings

Connection between depth and maximal elements in Apery sets

Enhanced understanding of the structure of affine semigroup rings

Abstract

We recall and delve into the different characterizations of the depth of an affine semigroup ring, providing an original characterization of depth two in three and four dimensional cases which are closely related to the existence of a maximal element in certain Apery sets.