English

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}
}