Nearly commuting matrices

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)199-218
Number of pages20
JournalJournal of Algebra
Volume497
DOIs
Publication statusPublished - Mar 1 2018

Keywords

  • Commuting matrices
  • F-purity
  • Frobenius
  • Singularities

ASJC Scopus subject areas

  • Algebra and Number Theory

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