Minimal free resolutions of monomial curves in P3k

Liasion of monomial curves in P3

“…Since/ l5 / 2 are binomials, it is not difficult to show s in [1] that a n is a power of either X 2 or X 3 with a 21 a power of the other X 2 or Ji 3 , while a 12 and a 22 are monomials, with coefficients +1. -^ϊ 1 · I n general, if A is an 2 χ 3 matrix, we let ^l.…”

“…Then R has a minimal graded resolution of the form, is an invariant of the odd linkage class of C. (See [7] for details. 1) was given in [1] for any monomial curve. 1) was given in [1] for any monomial curve.…”

“…We first describe the resolution in [1] for monomial curves, which is crucial for all the results in this paper. We first describe the resolution in [1] for monomial curves, which is crucial for all the results in this paper.…”

On the syzygies of quasi-complete intersection space curves

“…3 ] be the homogeneous ideal of a monomial curve in P 3 and let µ(I X ) be the number of elements in a minimal generating set of I X . In his paper ( [2]), Bresinsky proves that if µ(I X ) = µ ≥ 3, then I X has the following minimal free resolution:…”

“…On the other hand, we get n 1 < −(c 1 + m 2 ) since the dual of the exact sequence (2.2) Question 3.3. Bresinsky's work ( [2]) and Theorem 1.1 determine the structure of the minimal free resolutions of homogeneous ideals I X of monomial curves and quasi-complete intersections. What is the common generalization of monomial curves and quasi-complete intersections?…”