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Some remarks on varieties of pairs of commuting upper triangular matrices and an interpretation of commuting varieties

2008/03/05 by Roberta Basili, Basili, Roberta
Computer Science · Mathematics · Medicine · #14L30 #15A30 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Operator Algebras (math.OA) #Phytoestrogen effects and research #Tensor decomposition and applications #math.AG #math.OA #msc:14L30 #msc:15A30

paper · pdf · doi:10.48550/arxiv.0803.0722

Latex, 11 pages

openalex publication_date 2008/03/05 · arxiv created 2008/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that the variety of pairs of n x n commuting upper triangular matrices isn't a complete intersection for infinitely many values of n; we show that there exists m such that this happens if and only if n > m. We also show that m < 18 and that it could be found by determining the dimension of the variety of pairs of commuting strictly upper triangular matrices. Then we define a natural map from the variety of pairs of commuting n x n matrices onto a subvariety defined by linear equations of the grassmannian of subspaces of codimension 2 of a vector space of dimension n x n.

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