Polynomial Cubic Differentials and Convex Polygons in the Projective Plane
نویسندگان
چکیده
We construct and study a natural homeomorphism between the moduli space of polynomial cubic differentials of degree d on the complex plane and the space of projective equivalence classes of oriented convex polygons with d+3 vertices. This map arises from the construction of a complete hyperbolic affine sphere with prescribed Pick differential, and can be seen as an analogue of the Labourie– Loftin parameterization of convex RP structures on a compact surface by the bundle of holomorphic cubic differentials over Teichmüller space.
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