可解和无穷矩阵：可实现性及其相关变体的不可还原分解

arXiv - MATH - Commutative Algebra Pub Date : 2024-08-23 DOI:arxiv-2408.12784

Emiliano Liwski, Fatemeh Mohammadi

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引用次数: 0

摘要

我们介绍了可解 matroids 和 nilpotent matroids 族，并研究了它们的实现空间及其闭包。具体地说，我们分析了它们的相关品种及其不可还原分解。此外，我们还研究了一个称为弱无势矩阵的无势矩阵亚族，并计算了其相关矩阵变体的有限定义方程组。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Solvable and Nilpotent Matroids: Realizability and Irreducible Decomposition of Their Associated Varieties

We introduce the families of solvable and nilpotent matroids, and study their realization spaces and their closures. Specifically, we analyze their associated varieties and their irreducible decompositions. Additionally, we study a subfamily of nilpotent matroids, called weak nilpotent matroids, and compute a finite set of defining equations of their associated matroid varieties.

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arXiv - MATH - Commutative Algebra

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