Varieties of pairs of nilpotent matrices annihilating each other

2002/11/19 by Jan Schröer, Schröer, Jan
Mathematics · #14M99 #16G10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14M99 #msc:16G10

paper · pdf · doi:10.48550/arxiv.math/0211293

30 pages. This is an improved version of the originally submitted preprint

openalex publication_date 2002/11/19 · arxiv created 2003/11/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the irreducible components of the varieties V(n,a,b) of pairs (A,B) of matrices of size n such that AB = BA = 0 and A^a = B^b = 0.

Related

• Jordan forms for mutually annihilating nilpotent pairs
• The matrix equations XA-AX=X^αg(X) over fields or rings
• On the Irreducibility of Commuting Varieties of Nilpotent Matrices
• The variety of nilpotent pairs (A,B) with [A,B] = λI
• Mutually annihilating matrices, and a Cohen--Lenstra series for the nodal singularity