Abstract
We construct and study a natural homeomorphism between the moduli space of polynomial cubic dierentials of degree d on the complex plane and the space of projective equivalence classes of ori- ented convex polygons with d + 3 vertices. This map arises from the construction of a complete hyperbolic ane sphere with prescribed Pick dierential, and can be seen as an analogue of the Labourie-Loftin pa- rameterization of convex RP 2 structures on a compact surface by the bundle of holomorphic cubic dierentials over Teichmuller space.
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