Indecomposable syzygy-modules of high rank over hypersurface rings

In this paper we construct certain indecomposable syzygy modules over graded hypersurface rings and give a lower bound of their rank. Thereby we show that there is no upper bound for the ranks of the indecomposable maximal Cohen-Macaulay modules over a graded hypersurface ring of dimension at most two and of multiplicity at most three.