On the Cohen-Macaulay property for monomial curves in \({\mathbb{P}}^ 3_ k\) (Q798395)
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scientific article; zbMATH DE number 3869510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Cohen-Macaulay property for monomial curves in \({\mathbb{P}}^ 3_ k\) |
scientific article; zbMATH DE number 3869510 |
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On the Cohen-Macaulay property for monomial curves in \({\mathbb{P}}^ 3_ k\) (English)
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1984
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The arithmetical Cohen-Macaulay property for monomial curves in \({\mathbb{P}}^ 3_ k\) with generic zero \((t_ 0^{n_ 3},t_ 0^{n_ 3-n_ 1}t_ 1^{n_ 1},t_ 0^{n_ 3-n_ 2}t_ 1^{n_ 2},t_ 1^{n_ 3})\), \(0<n_ 1<n_ 2<n_ 3\) integers such that \((n_ 1,n_ 2,n_ 3)=1\), is known to hold if \(n_ 3>(n_ 2-1)(n_ 2-n_ 1)\) [see for instance the author's paper in Manuscr. Math. 47, 105-132 (1984; Zbl 0547.13014)]. In the present paper necessary and sufficent arithmetic conditions, in terms of a continued fraction expansion depending on \(n_ 1,n_ 2,n_ 3\) are given, in order for the indicated curves not to be arithmetically Cohen-Macaulay.
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Cohen-Macaulay property for monomial curves
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