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ABSTRACT. The system of Weierstrass polynomials, defined originally for ideals in convergent power series rings, together with its sequence of degrees allows us to analyze a homogeneous ideal directly. Making use of it, we study local cohomology modules, syzygies, and then graded Buchsbaum rings. Our results give a formula which to some extent clarifies the connection among the matrices appearing in the free resolution starting from a system of Weierstrass polynomials, a rough classification of graded Buchsbaum rings in the general case and a complete classification of graded Buchsbaum integral domains of codimension two.

Definition 1.4]) and classified arithmetically Buchsbaum curves with nontrivial deficiency modules in terms of their basic sequences. But there, an important problem was left unconsidered; to find a necessary and sufficient condition for the existence of integral arithmetically Buchsbaum curves with a given basic sequence. The aim of this paper is to give a complete answer to this problem in the case where the base field has characteristic zero.