  Let M be a non-compact hyperbolic 3-manifold that has a triangulation by
positively oriented ideal tetraedra. We explain how to produce local
coordinates for the variety defined by the gluing equations for
PGL(3,C)-representations. In particular we prove local rigidity of the
"geometric" representation in PGL(3,C), recovering a recent result of
Menal-Ferrer and Porti. More generally we give a criterion for local rigidty of
PGL(3,C)-representations and provide detailed analysis of the figure eight knot
sister manifold exhibiting the different possibilities that can occur.
