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 |
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Keywords
- Commuting matrices
- F-purity
- Frobenius
- Singularities
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Nearly commuting matrices. / Kadyrsizova, Zhibek.
In: Journal of Algebra, Vol. 497, 01.03.2018, p. 199-218.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nearly commuting matrices
AU - Kadyrsizova, Zhibek
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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.
KW - Commuting matrices
KW - F-purity
KW - Frobenius
KW - Singularities
UR - http://www.scopus.com/inward/record.url?scp=85035115221&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85035115221&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2017.10.019
DO - 10.1016/j.jalgebra.2017.10.019
M3 - Article
VL - 497
SP - 199
EP - 218
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -