### The Variety of Pairs of Matrices with $\operatorname{rank}(AB - BA) \leq 1$

Authors and Corporations: The Variety of Pairs of Matrices with $\operatorname{rank}(AB - BA) \leq 1$ Proceedings of the American Mathematical Society, 105, 1989, 4, p. 787-792 American Mathematical Society 787-792 1088-6826 0002-9939

We will show that the variety of pairs of $n \times n$ matrices over an algebraically closed field with rank one commutator consists of $n - 1$ irreducible components each of dimension $n^2 + 2n - 1$.

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