  Let X and Y be commuting nilpotent K-endomorphisms of a vector space V, where
K is a field of characteristic p >= 0. If F=K(t) is the field of rational
functions on the projective line, consider the K(t)-endomorphism A=X+tY of V.
If p=0, or if the (p-1)-st power of A is 0, we show here that X and Y are
tangent to the unipotent radical of the centralizer of A in GL(V). For all
geometric points (a:b) of a suitable open subset of the projective line, it
follows that X and Y are tangent to the unipotent radical of the centralizer of
aX+bY. This answers a question of J. Pevtsova.
