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dimension filtration; sequentially Cohen-Macaulay filtration; cohomological dimension; bigraded module; Cohen-Macaulay module
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.
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