发表机构
Faculty of Mathematics, University of Education, Hue University（富牌大学教育学院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在特征零域上，通过有限数值检验刻画了四变量Artinian商中决定一般初始理想的Hilbert函数，推广了拟对称条件，并给出标准单项式与极小生成元的非递归公式。
AI 中文摘要
在特征为零的域上，我们刻画了在四变量且具有$2$-强Lefschetz性质的Artinian商中，决定度反向字典序一般初始理想的Hilbert函数。我们的判据是一个有限的数值检验，严格推广了Harima和Wachi的拟对称条件。证明通过它们共同的三变量截面上的Borel序中的下集旗来参数化可能的一般初始理想。我们还给出了几乎反向字典序理想的标准单项式和极小生成元的非递归公式，并将其特化到至多四变量且无次数限制的一般完全交。
英文摘要
Over a field of characteristic zero, we characterize the Hilbert functions that determine the degree reverse lexicographic generic initial ideal among Artinian quotients in four variables with the $2$-strong Lefschetz property. Our criterion is a finite numerical test that strictly extends the quasi-symmetry condition of Harima and Wachi. The proof parametrizes the possible generic initial ideals by flags of lower sets in the Borel orders on their common three-variable section. We also give nonrecursive formulas for the standard monomials and minimal generators of the almost reverse lexicographic ideal, and specialize them to generic complete intersections in at most four variables without restrictions on the degrees.
Comments14 pages
