  In this paper we construct a compactification for the parameter space of
convex projective structures on a fixed n-manifold M. This parameter space is a
closed semi-algebraic subset of the variety of characters of representations of
the fundamental group of M in SL_{n+1}(R). The boundary is the inverse limit of
an inverse system of logarithmic limit sets of this semi-algebraic set, in a
sense it is the tropicalization of the parameter space. The interpretation of
the boundary points can also be given using tropical geometry. This
construction is a generalization of the construction of compactification of the
Teichm\"uller spaces.

Geometric Topology;Algebraic Geometry