On the variety of almost commuting nilpotent matrices

2009/03/11 by Eliana Zoque, Zoque, Eliana
Computer Science · Engineering · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Representation Theory (math.RT) #graph theory and CDMA systems #math.RT

paper · pdf · doi:10.48550/arxiv.0903.2032

arxiv created 2009/03/11 · openalex publication_date 2009/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the variety of n by n matrices with commutator of rank at most one. We describe its irreducible components; two of them correspond to the pairs of commuting matrices, and n-2 components of smaller dimension corresponding to the pairs of rank one commutator. In our proof we define a map to the zero fiber of the Hilbert scheme of points and study the image and the fibers.

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