Generators for the ideal of an arithmetically Buchsbaum curve (Q912944)

The authors continue their study of arithmetically Buchsbaum curves C in \({\mathbb{P}}^ 3\). Relating the \(curve\quad C\) to its hyperplane sections and its Hartshorne-Rao module they obtain interesting bounds for the number and degrees of the generators of the defining ideal \(of\quad C.\) Some of them were first proved by \textit{M. Amasaki} with different methods. The results are discussed by various examples. For some generalizations we refer to the characterization of arithmetically Buchsbaum subschemes of \(co\dim eosion\quad 2\) in \({\mathbb{P}}^ n\), due to \textit{M. Chang} [J. Differ. Geometry 31, No.2, 323-341 (1990; Zbl 0663.14034)]. The paper concludes with a characterization of the divisor classes on a smooth cubic surface corresponding to arithmetically Cohen-Macaulay and Buchsbaum curves. This extends earlier work of \textit{M. Watanabe} [Tokyo J. Math. 4, 331-341 (1981; Zbl 0496.14032)].