On the variety of almost commuting nilpotent matrices

Eliana Zoque

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arXiv · 0903.2032

On the variety of almost commuting nilpotent matrices

Eliana Zoque

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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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BibTeX RIS

Eliana Zoque. 2009-03-11. On the variety of almost commuting nilpotent matrices. https://arxiv.org/abs/0903.2032

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