SEQUENTIALLY COHEN-MACAULAYNESS OF BIGRADED MODULES

Let K be a field, S = K[x(1), ..., x(m),y(1,) ..., y(n]) a standard bigraded polynomial ring, and M a finitely generated bigraded S -module. In this paper, we study the sequentially Cohen-Macaulayness of M with respect to Q =(y(1), ..., y(n) ). We characterize the sequentially CohenMacaulayness of L circle times(K) N with respect to Q as an S-module when L and N are non -zero finitely generated graded modules over K[x(1), ..., x(m)] K[y(1) ,..., y(n)] and respectively. All hypersurface rings that are sequentially Cohen -Macaulay with respect to Q are classified.