Minimal Free Resolutions of Zero-dimensional Schemes in P<em>1</em> *P<em>1</em>

• 作者: Paola Bonacini Lucia Marino
• 来源期刊: 代数集刊:英文版
• 学科: 工学
• 关键词: 零维 免费 希尔伯特 曲线分割 ACM 分辨率 发电机
• 年，卷（期）: 2015,（1）
• 页码范围: 97-108
• 页数: 12页
• 分类号: TB383
• 语种: 中文

摘要

Let X be a zero-dimensional scheme in p1 * p1. Then X has a minimal free resolution of length 2 if and only if X is ACM. In this paper we determine a class of reduced schemes whose resolutions, similarly to the ACM case, can be obtained by their Hilbert functions and depend only on their distributions of points in a grid of lines. Moreover, a minimal set of generators of the ideal of these schemes is given by curves split into the union of lines.