论文标题
斯坦纳系统和点的配置
Steiner systems and configurations of points
论文作者
论文摘要
本文的目的是在设计理论与代数几何/交换代数之间建立联系。特别是，如果有任何施泰纳系统$ s（t，n，v）$，我们将两个理想与合适的多项式戒指相关联，以定义点的施纳键配置及其补充。我们专注于后者，研究其同源不变，例如Hilbert功能和Betti数字。我们还研究了与理想相关的符号和常规力量，以定义点的施料构造的补充，发现其waldschmidt常数，规律性，其复苏和渐近复活的边界。我们还计算了与任何施泰纳的任何点配置及其补充相关的线性代码的参数。
The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System $S(t,n,v)$ we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configuration of points and its Complement.
