Sequentially generalized Cohen–Macaulayness of bigraded modules

Let S = K[x1,…,xm, y1,…,yn] 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 = (y1,…,yn). We prove that if I ⊆ S be a monomial ideal with cd (Q, S/I) ≤ 2, then S/I is sequentially generalized Cohen–Macaulay with respect to Q.