  We consider the variety of $(p+1)$-tuples of matrices $A_j$ (resp. $M_j$)
from given conjugacy classes $c_j\subset gl(n,{\bf C})$ (resp. $C_j\subset
GL(n,{\bf C})$) such that $A_1+... +A_{p+1}=0$ (resp. $M_1... M_{p+1}=I$). This
variety is connected with the weak {\em Deligne-Simpson problem: give necessary
and sufficient conditions on the choice of the conjugacy classes $c_j\subset
gl(n,{\bf C})$ (resp. $C_j\subset GL(n,{\bf C})$) so that there exist
$(p+1)$-tuples with trivial centralizers of matrices $A_j\in c_j$ (resp.
$M_j\in C_j$) whose sum equals 0 (resp. whose product equals $I$).} The
matrices $A_j$ (resp. $M_j$) are interpreted as matrices-residua of Fuchsian
linear systems (resp. as monodromy operators of regular linear systems) on
Riemann's sphere. We consider examples of such varieties of dimension higher
than the expected one due to the presence of $(p+1)$-tuples with non-trivial
centralizers; in one of the examples the difference between the two dimensions
is O(n).
