标题： 多重复数配置：Gorenstein联络的一个案例研究 显示英文标题

标题： Multicomplex Configurations: a case study in Gorenstein Liaison

摘要： 我们引入并研究多复数配置，这是一类通过阿廷单项式理想极化的特殊化构造的射影代数簇。 在几何极化和几何顶点分解的基础上，我们建立了这些配置保留良好代数性质的条件。 特别是，我们证明了在适当选择线性形式进行替换的情况下，所得的理想具有预定初始理想的格罗布纳基，并且属于一个完全交的戈伦斯坦联络类。 显示英文摘要

摘要： We introduce and investigate multicomplex configurations, a class of projective varieties constructed via specialization of the polarizations of Artinian monomial ideals. Building upon geometric polarization and geometric vertex decomposition, we establish conditions under which such configurations retain desirable algebraic properties. In particular, we show that, given suitable choices of linear forms for substitution, the resulting ideals admit Gr\"obner bases with prescribed initial ideals and are in the Gorenstein liaison class of a complete intersection.