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ISSN 1088-6826(online) ISSN 0002-9939(print)



Hyperplane sections of arithmetically Cohen-Macaulay curves

Author: Charles H. Walter
Journal: Proc. Amer. Math. Soc. 123 (1995), 2651-2656
MSC: Primary 14H99; Secondary 14M10
MathSciNet review: 1260185
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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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Keywords: Arithmetically Cohen-Macaulay, hyperplane section, local complete intersection, normal bundle
Article copyright: © Copyright 1995 American Mathematical Society

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