On the structure of sequentially Cohen--Macaulay bigraded modules

Let $K$ be a field and $S=K[x_1,\dots ,x_m,y_1,\dots ,y_n]$ 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 $Q=(y_1,\dots ,y_n)$. 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.