On the structure of sequentially Cohen--Macaulay bigraded modules

TL;DR

This paper characterizes the structure of sequentially Cohen--Macaulay bigraded modules over a polynomial ring, providing explicit descriptions and local cohomology characterizations, advancing understanding of their algebraic properties.

Contribution

It explicitly describes the structure of sequentially Cohen--Macaulay bigraded modules and characterizes them via local cohomology modules, a novel approach in this context.

Findings

Explicit structure description of sequentially Cohen--Macaulay modules

Characterization via local cohomology modules

Application to Cohen--Macaulay modules that are sequentially Cohen--Macaulay

Abstract

Let $K$ be a field and $S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]$ be the standard bigraded polynomial ring over $K$. In this paper, we explicitly describe the structure of finitely generated bigraded "sequentially Cohen--Macaulay" $S$-modules with respect to $Q=(y_1,\ldots,y_n)$. Next, we give a characterization of sequentially Cohen--Macaulay modules with respect to $Q$ in terms of local cohomology modules. Cohen--Macaulay modules that are sequentially Cohen--Macaulay with respect to $Q$ are considered.