Hyperplane sections of arithmetically Cohen-Macaulay curves

Walter, Charles H.

doi:10.1090/S0002-9939-1995-1260185-2

Hyperplane sections of arithmetically Cohen-Macaulay curves
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Proc. Amer. Math. Soc. 123 (1995), 2651-2656 Request permission

Abstract:

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

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