Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 199-218 |
| Number of pages | 20 |
| Journal | Journal of Algebra |
| Volume | 497 |
| DOIs | |
| Publication status | Published - Mar 1 2018 |
Keywords
- Commuting matrices
- F-purity
- Frobenius
- Singularities
ASJC Scopus subject areas
- Algebra and Number Theory
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Cite this
Kadyrsizova, Z. (2018). Nearly commuting matrices. Journal of Algebra, 497, 199-218. https://doi.org/10.1016/j.jalgebra.2017.10.019