发表机构
Kennesaw State University（肯尼索州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明任意尺寸下永久型簇的维数公式，并得出永久式临界轨迹的余维数及极大永久式生成完全交的约化性。
AI 中文摘要
设 $I_h(a,b)$ 为由特征不等于二的域上一般 $a\times b$ 矩阵的 $h\times h$ 永久式生成的理想。我们证明当 $1\le h\le\min(a,b)$ 且 $h<\max(a,b)$ 时，$\dim K[X]/I_h(a,b)=\max(a,b)(h-1)$。因此，$n$ 阶永久式的临界轨迹对每个 $n\ge 2$ 具有余维数 $2n$。我们还证明一般 $k\times(k+1)$ 矩阵的极大永久式生成一个几何约化的完全交。维数论证使用枢轴展开和边界变量中的三次关系。与最高次方程的两次连续比较将相关纤维简化为坐标支撑计算。约化性由独立的正则序列论证和排除例外轨迹上分量的维数估计得出。
英文摘要
Let $I_h(a,b)$ be the ideal generated by the $h\times h$ permanents of a generic $a\times b$ matrix over a field of characteristic different from two. We prove that $\dim K[X]/I_h(a,b)=\max(a,b)(h-1)$ whenever $1\le h\le\min(a,b)$ and $h<\max(a,b)$. Consequently, the critical locus of the permanent of order $n$ has codimension $2n$ for every $n\ge 2$. We also prove that the maximal permanents of a generic $k\times(k+1)$ matrix generate a geometrically reduced complete intersection. The dimension argument uses a pivot expansion and cubic relations in the border variables. Two successive comparisons with highest-degree equations reduce the relevant fibers to a coordinate-support calculation. Reducedness follows from a separate regular-sequence argument and a dimension estimate excluding components over the exceptional locus.
