On the variety of almost commuting nilpotent matrices

Details On the variety of almost commuting nilpotent matrices On the variety of almost commuting nilpotent matrices

2009-03-11

arxiv.org/abs/0903.2032v1

Mathematics

Representation Theory

Scientific paper

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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