Sequentially generalized Cohen-Macaulayness of bigraded modules

Let S = K[x(1),..., x(m), y(1),..., y(n)] be the standard bigraded polynomial ring over a field K, and M a finitely generated bigraded S-module. In this paper we study the generalized Cohen-Macaulayness and sequentially generalized Cohen-Macaulayness of M with respect to Q = (y(1),..., y(n)). We prove that if I subset of S be a monomial ideal with cd(Q, S/I) <= 2, then S/I is sequentially generalized Cohen-Macaulay with respect to Q.