Varieties of pairs of nilpotent matrices annihilating each other

Abstract

We classify the irreducible components of the varieties

V (n, a, b) = {(A, B) \in M_{n} (K) \times M_{n} (K) ∣ A B = B A = A^{a} = B^{b} = 0} .

Jan Schröer, Varieties of pairs of nilpotent matrices annihilating each other. Comment. Math. Helv. 79 (2004), no. 2, pp. 396–426