  Consider the projective variety $X_\lambda$ of binary forms of degree $d$
whose linear factors are distributed according to the partition $\lambda$ of
$d$. We determine minimal sets of local generators of the fiber product of
$X_\lambda$ with its normalization, and we show that the local Jacobian
matrices of this product contain the product of the identity matrix of maximal
rank with a unit. We use this to fill a gap in a crucial proof in Chipalkatti's
"On equations defining Coincident Root Loci". Also, we give a new description
of the singular locus of $X_\lambda$ and a criterion for the smoothness of
$X_\lambda$.
