二元线性系统的重构与稀疏Krylov层的剖面几何
Reconstruction of Binary Linear Systems and Profile Geometry of Sparse Krylov Strata
浏览论文内容
中文总结 AI 辅助
本文研究二元线性系统除子概形的重构与稀疏Krylov层的剖面几何，提出函子性重构方法、算术剖面分类及正规性判据，统一了稀疏Krylov秩轨迹的框架。
中文摘要 AI 辅助
我们研究了二元线性系统的除子概形及其稀疏Krylov图的重构与剖面几何。在整数环上，完全嵌入除子概形的首个非零方程在任意基变换下函子性地恢复定义线性系统，从而给出从线性系统的Grassmannian到相应Hilbert概形的闭浸入。在特征零的单项式系统中，算术剖面分类了约化分解分支，确定了它们的像维数和一般重数，并控制了几何约化性。对于完全等差数列，关系分支及其像的规范化是带有两个自然极化的射影空间的显式乘积。我们给出了一个基于相关Fourier数据的仿射正规性判据，以及一个通过附加端点分配条件得到的射影判据。这些结果将闭稀疏Krylov秩轨迹置于统一的“重构-规范化”框架中，并产生了显式的混合次数和形式剖面推论。它们也阐明了仅规范化数据的极限：恢复一个可能非正规的像代数需要此处未涉及的额外信息。
英文摘要
We study reconstruction and profile geometry for divisor schemes of binary linear systems and their sparse Krylov charts. Over the integers, the first nonzero equations of the complete embedded divisor scheme recover the defining linear system functorially under arbitrary base change, yielding a closed immersion from the Grassmannian of linear systems to the corresponding Hilbert scheme. For monomial systems in characteristic zero, arithmetic profiles classify the reduced factorization branches, determine their image dimensions and generic multiplicities, and control geometric reducedness. For complete progressions, the normalizations of the relation branches and their images are explicit products of projective spaces equipped with two natural polarizations. We give an affine normality criterion in terms of the associated Fourier data and a projective criterion obtained by adjoining an endpoint-allocation condition. These results place the closed sparse Krylov rank loci in a uniform reconstruction--normalization framework and yield explicit mixed-degree and formal-profile consequences. They also clarify the limit of normalization data alone: recovering a possibly nonnormal image algebra requires additional information not addressed here.
发表机构
- South China Normal University（华南师范大学）
机构由 AI 辅助整理，请以论文原文为准。
