Varieties of pairs of nilpotent matrices annihilating each other
Jan Schröer
University of Leeds, UK

Abstract
We classify the irreducible components of the varieties
\[ \V(n,a,b) = \{ (A,B) \in \M_n(\field) \times \M_n(\field) \mid AB = BA = A^a = B^b = 0 \}. \]Cite this article
Jan Schröer, Varieties of pairs of nilpotent matrices annihilating each other. Comment. Math. Helv. 79 (2004), no. 2, pp. 396–426
DOI 10.1007/S00014-003-0788-3