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

A compactification for the spaces of convex projective structures on manifolds