Hyperplane sections of arithmetically Cohen-Macaulay curves

Abstract

We show that for every r ≥ 4 r \geq 4 there exists a d r {d_r} such that for all d ≥ d r d \geq {d_r} a general set of r points in P r − 1 {{\mathbf {P}}^{r - 1}} is not a hyperplane section of an arithmetically Cohen-Macaulay local complete intersection curve in P r {{\mathbf {P}}^r} . Explicit values for the bound d r {d_r} are given. In particular, for r ≥ 12 r \geq 12 we have d r = r + 3 {d_r} = r + 3 , and this bound is exact.