发表机构
Indian Institute of Science Education and Research; University of Nebraska–Lincoln（印度科学教育研究所; 内布拉斯加大学林肯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对一般矩阵的线性基变换群作用下的GL不变理想，确定其普通幂、饱和理想、符号幂，给出两类渐近不变量的显式公式，证明相关广义符号Rees代数是Noether的。
AI 中文摘要
本研究涉及在一般矩阵的线性基变换群作用下保持不变的理想，我们将其称为GL不变理想。我们确定了这类理想的普通幂、关于行列式理想的饱和理想，以及符号幂；给出了称为（斜）Waldschmidt常数和渐近复苏的渐近不变量的显式公式，这些不变量用于衡量这类理想族的增长并比较普通拓扑与符号拓扑；还证明了与这类理想相关的广义符号Rees代数是Noether的。
英文摘要
This work concerns ideals invariant under the action of the group of linear base changes on a generic matrix; we call these GL-invariant ideals. We determine the ordinary powers, their saturations with respect to determinantal ideals, and the symbolic powers of GL-invariant ideals. We give explicit formulas for asymptotic invariants known as (skew) Waldschmidt constants and asymptotic resurgence, which measure the growth of these families and compare the ordinary and symbolic topologies. We also prove that the generalized symbolic Rees algebras associated with these ideals are Noetherian.
