  In the Simpson moduli space $M$ of semi-stable sheaves with Hilbert
polynomial $dm-1$ on a projective plane we study the closed subvariety $M'$ of
sheaves that are not locally free on their support. We show that for $d\ge 4$
it is a singular subvariety of codimension $2$ in $M$. The blow up of $M$ along
$M'$ is interpreted as a (partial) modification of $M\setminus M'$ by vector
bundles (on support).
