阶梯或区间行列式模块的吹胀代数

arXiv - MATH - Commutative Algebra Pub Date : 2024-08-04 DOI:arxiv-2408.01903

Kuei-Nuan Lin, Yi-Huang Shen

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引用次数: 0

摘要

我们确定了多雷瑟尔基团及其特殊纤维环的表征理想的 Gr\"{o}bner 基。具体地说，我们关注的模块是由两边梯形矩阵的最大最小值或单位区间行列式理想产生的理想的直和。我们的分析表明，多布尔代数是科斯祖尔-科恩-麦考莱正域，在零特征中具有有理奇点，并且在正特征中是 F 有理的。

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Blowup algebras of ladder or interval determinantal modules

We determine Gr\"{o}bner bases for the presentation ideals of multi-Rees algebras and their special fiber rings. Specifically, we focus on modules that are direct sums of ideals generated by either maximal minors of a two-sided ladder matrix or unit interval determinantal ideals. Our analysis reveals that the multi-blowup algebras are Koszul Cohen--Macaulay normal domains, possess rational singularities in characteristic zero, and are F-rational in positive characteristic.

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arXiv - MATH - Commutative Algebra

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