Generators for the ideal of an arithmetically Buchsbaum curve
Generators for the ideal of an arithmetically Buchsbaum curve
复制标题
算术布克斯鲍姆曲线理想值的生成器
DOI：
10.1016/0022-4049(89)90155-2
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发表时间：
1989
影响因子：
0.8
通讯作者：
J. Migliore
中科院分区：
文献类型：
--
作者：
A. Geramita;J. Migliore
本文继续研究p3中的算术Buchsbaum曲线的超平面截面。这里我们特别关心的关系的最小发电机的理想曲线C和理想的超平面部分C∩h .通过分析这些理想的结构(Hartshorne-Rao模块密切相关(C))我们可以给两个不等式的数量最少的发电机的理想C(原定M . Amasaki;第二个是我们给一个新的以及更短的证明。)我们还展示了第二个不等式如何立即给出包含C的曲面的最小次的Amasaki界。这些考虑产生了关于C的一些结果，例如特性e (C)的指标界。最后，我们应用这些技术对光滑三次曲面上的算术Cohen-Macaulay和Buchsbaum曲线进行分类。
This paper continues the study of arithmetically Buchsbaum curves in P 3 by focusing on their hyperplane sections. Here we are especially concerned with the relation between the minimal generators of the ideal of such a curve C and those of the ideal of its hyperplane section C∩ H. By analyzing the structure of these ideals (which are closely related to the Hartshorne—Rao module M (C)) we are able to give two inequalities for the number of minimal generators of the ideal of C.(The second is originally due to M. Amasaki; we give a new and shorter proof of it.) We also show how the second inequality immediately gives Amasaki's bound for the least degree of a surface containing C. These considerations yield a number of results about C, for instance bounds on the index of speciality e (C). Finally, we apply these techniques to classify the arithmetically Cohen—Macaulay and Buchsbaum curves on a smooth cubic surface.