On the variety of almost commuting nilpotent matrices
Representation Theory
2009-03-12 v1
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.
Keywords
Cite
@article{arxiv.0903.2032,
title = {On the variety of almost commuting nilpotent matrices},
author = {Eliana Zoque},
journal= {arXiv preprint arXiv:0903.2032},
year = {2009}
}