  There is a canonical identification, due to the author, of a convex real
projective structure on an orientable surface of genus g and a pair consisting
of a conformal structure together with a holomorphic cubic differential on the
surface. The Deligne-Mumford compactification of the moduli space of curves
then suggests a partial compactification of the moduli space of convex real
projective structures: Allow the Riemann surface to degenerate to a stable
nodal curve on which there is a regular cubic differential. We construct convex
real projective structures on open surfaces corresponding to this singular data
and relate their holonomy to earlier work of Goldman. Also we have results for
families degenerating toward the boundary of the moduli space. The techniques
involve affine differential geometry results of Cheng-Yau and C.P. Wang and a
result of Dunkel on the asymptotics of systems of ODEs.
