Communications of the
Korean Mathematical Society CKMS

We give an upper bound for the degrees of the nonvanishing homology modules of the Schur complex $L_{\lambda/ \mu} \phi$ in terms of the depths of the determinantal ideals of $\phi.$ Using this fact, we obtain the acyclic theorem for $L_{\lambda}\phi$ and the information concerning the support of the homology modules of $L_{\lambda/\mu}\phi.$

Keywords: determinantal ideal, minimal free resolution, Schur \linebreak complex

MSC numbers: 13D02, 13D03