Nearly commuting matrices

JOURNAL OF ALGEBRA

卷:497

Article

Kadyrsizova, Zhibek¹ 

[1] Nazarbayev Univ, Sch Sci & Technol, Dept Math, 53 Kabanbay Batyr Ave, Astana 010000, Kazakhstan

关键词: Frobenius;    Singularities;    F-purity;    Commuting matrices;   

DOI  :  10.1016/j.jalgebra.2017.10.019

来源: Elsevier

【 摘 要 】

We prove that the algebraic set of pairs of matrices with a diagonal commutator over a field of positive prime characteristic, its irreducible components, and their intersection are F-pure when the size of matrices is equal to 3. Furthermore, we show that this algebraic set is reduced and the intersection of its irreducible components is irreducible in any characteristic for pairs of matrices of any size. In addition, we discuss various conjectures on the singularities of these algebraic sets and the system of parameters on the corresponding coordinate rings. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free