Relative Cohen-Macaulayness and relative unmixedness of bigraded modules

TL;DR

This paper investigates properties of finitely generated bigraded modules over a polynomial ring, focusing on their relative Cohen-Macaulayness and unmixedness, and extends Reisner's criterion to this context.

Contribution

It introduces a generalization of Reisner's criterion for Cohen-Macaulay simplicial complexes to the setting of bigraded modules, advancing the theoretical understanding.

Findings

Characterization of relative Cohen-Macaulay modules

Extension of Reisner's criterion to bigraded modules

Insights into the structure of bigraded modules

Abstract

In this paper we study the finitely generated bigraded modules over a standard bigraded polynomial ring which are relative Cohen-Macaulay or relative unmixed with respect to one of the irrelevant bigraded ideals. A generalization of Reisner's criterion for Cohen-Macaulay simplicial complexes is considered.