Nearly Commuting Matrices
Commutative Algebra
2017-12-15 v2 Algebraic Geometry
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 -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.
Cite
@article{arxiv.1705.10957,
title = {Nearly Commuting Matrices},
author = {Zhibek Kadyrsizova},
journal= {arXiv preprint arXiv:1705.10957},
year = {2017}
}
Comments
30 pages, improved the exposition and some of the proofs, to appear in the Journal of Algebra