A study of three codimensional graded Buchsbaum domains

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1. A computer program has been made that enables us to find the candidates for the system of minimal generators of the generic initial ideal of a three codimensional Cohen-Macaulay homogeneous ideal in a polynomial ring, with the use of its basic sequence. It is useful because the first three parts of the basic sequence of a three codimensional homogeneous ideal defining a graded Buchsbaum ring coincides with the basic sequence of a three codimensional homogeneous ideal defining a graded Cohen-Macaulay ring.2. We have been trying to construct an integral arithmetically Buchsbaum curve on a nonsingular hypersurface in the four dimensional projective space, with the help of the usual Bourbaki sequence associated with the maximal Buchsbaum graded module obtained by taking the minimal free resolution of the ground field. By our past results, we know all possible basic sequences of arithmetically Buchsbaum curves, but we have not yet been able to check by this method which sequences correspond to integral curves. The difficulty seems to come from the lack of complete knowledge of maximal Cohen-Macaulay modules on R/(f).3. In order to reconsider the two codimensional case, a lot of our informal results obtained in the past on the basic sequences of integral curves in the three dimensional projective space, have now been written in a paper. Further, applying the above mentioned computer program to this case, we have found that the condition proposed by Cook and the set of conditions described in this paper together make a better set of necessary conditions for the basic sequence of an integral curve in the three dimensional projective space to satisfy.