On liaison, arithmetical Buchsbaum curves and monomial curves in P3

On Buchsbaum simplicial affine semigroups

“…The elements n ∈ S for which G n is not connected are (3, 2), (6, 2), (4,3) and (2,4). n = n r+t +n j = n r+s +n i = (m+n i )+n j = (m+n j )+n i , which implies that n r+s ∈ [n r+t ] and thus #[n r+t ] = r = #[n − n i ].…”

“…Let S = (2, 0), (0, 2), (3,1), (1,3), (1,2) . Using the procedure presented in [10] to compute r i=1 S(n i ) = S((2, 0)) ∩ S((0, 2)), we get S((2, 0)) ∩ S((0, 2)) = {(0, 0), (3, 1), (1, 3), (1, 2), (4, 3), (2, By looking at [(3, 1)], the only possible candidate to be m is (1, 1).…”

On the Structure of Arithmetically Buchsbaum Curves in $\mathrm P^3_k$

“…Since T is a thin subspace of S(a; m, n), it may well be hoped that the curves K~I(S) for s^S(a; in, n) general are nonsingular and irreducible, however we have not confirmed it as yet. B. by [5] and its short basic sequence is (2; -; 2n+l). It therefore coincides with TT~I(S) for a certain point seS(2; -; 2n+l).…”

Determinantal Ideals and Monomial Curves in the Three-Dimensional Space

“…Cohen-Macaulay curves in P 3 , which are defined by the vanishing of the 2-minors of a 2 × 3 matrix (see [4] or [11], and [5] or [14]). In this paper we first describe a class of ideals, generated by the maximal minors of a two-row matrix, whose variety is defined by the vanishing of a proper subset of the generating minors; then we show that the defining ideal of any monomial curve in K 3 or P 3 contains the ideal of 2-minors of a 2 × 3 matrix that is a set-theoretic complete intersection on two of these minors.…”