  We suggest a geometrical approach to the semi-invariants of quivers based on
Luna's slice theorem and the Luna-Richardson theorem. The locally semi-simple
representations are defined in this spirit but turn out to be connected with
stable representations in the sense of GIT, Schofield's perpendicular
categories, and Ringel's regular representations. As an application of this
method we obtain an independent short proof of the theorem of Skowronsky and
Weyman about semi-invariants of the tame quivers.
