Steiner系统和点的构型
Steiner systems and configurations of points
摘要：
本文的目的是使设计理论和代数几何/交换代数之间的联系。特别地，给定任何Steiner系统$S(t,n,v)$，我们在一个合适的多项式环中关联两个理想，定义点的Steiner配置及其补。我们重点研究后者，研究它的同调不变量，如Hilbert函数和贝蒂数。我们还研究了象征性的和经常性的权力与理想定义一个补充的施泰纳配置的点，发现其Waldschlavian常数，规律性，其复苏和渐近复苏的界限。我们还计算了与点的任何Steiner配置及其补相关的线性码的参数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
