Abstract
The arithmetical Cohen-Macaulay property for monomial curves in ℙ 3 K with generic zero\((t_0^{n_3 } ,t_0^{n_3 - n_1 } t_0^{n_1 } ,t_0^{n_3 - n_2 } t_0^{n_2 } ,t_0^{n_3 } )\) was shown in [2] to be true forn 3>(n 2−1)(n 2−n 1),n 3>n 2, (n 1,n 2,n 3)=1. Here we establish necessary and sufficient arithmetic conditions in terms ofn 1,n 2,n 3 in order for the indicated curves not to be arithmetically Cohen-Macaulay.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bresinsky, H.: Minimal free resolutions of monomial curves in ℙ 3 k . Linear Algebra and Appl.59, 121–129 (1984).
Bresinsky, H.: Monomial Buchsbaum ideals in ℙr. Manuscripta Math.47, 105–132 (1984).
Bresinsky, H., Renschuch, B.: Basisbestimmung Veronesescher Projektionsideale mit allgemeiner Nullstelle (t m0 ,t m−r0 t r1 ,t m−s0 t s1 ,t m1 ). Math. Nachr.96, 257–269 (1980).
Bresinsky, H., Schenzel, P., Vogel, W.: On liaison, arithmetical Buchsbaum curves and monomial curves in ℙ3. J. Algebra86, 283–301 (1984).
Herzog, J.: Generators and relations of Abelian semigroups and semigroup rings. Manuscripta Math.3, 175–193 (1970).
Perron, O.: Die Lehre von den Kettenbrüchen. New York: Chelsea 1950.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bresinsky, H. On the Cohen-Macaulay property for monomial curves in ℙ 3 K . Monatshefte für Mathematik 98, 21–28 (1984). https://doi.org/10.1007/BF01536905
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01536905