Local cohomology tables of sequentially almost Cohen-Macaulay modules

TL;DR

This paper introduces sequentially almost Cohen-Macaulay modules over polynomial rings and characterizes the extremal rays of their local cohomology tables, providing insights into their structural decompositions.

Contribution

It defines the class of sequentially almost Cohen-Macaulay modules and describes the extremal rays of their local cohomology cones, advancing understanding of their cohomological structure.

Findings

Characterization of extremal rays of local cohomology cones

Description of decompositions of local cohomology tables in dimension 3

Introduction of sequentially almost Cohen-Macaulay modules

Abstract

Let $R$ be a polynomial ring over a field. We introduce the concept of sequentially almost Cohen-Macaulay modules and describe the extremal rays of the cone of local cohomology tables of finitely generated graded $R$-modules which are sequentially almost Cohen-Macaulay, and describe some cases when the local cohomology table of a module of dimension 3 has a nontrivial decomposition.