  We consider the variety of $(p+1)$-tuples of matrices $M_j$ from given
conjugacy classes from $GL(n,{\bf C})$ such that $M_1... M_{p+1}=I$. This
variety is connected with the Deligne-Simpson problem and the matrices $M_j$
are interpreted as monodromy operators of regular systems on Riemann's sphere.
We consider among others cases when the dimension of the variety is higher than
the expected one due to the presence of $(p+1)$-tuples with non-trivial
centralizers.
