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arXiv · 1407.8149

Polynomial cubic differentials and convex polygons in the projective plane

David Dumas·Michael Wolf
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Abstract

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^2 structures on a compact surface by the bundle of holomorphic cubic differentials over Teichmuller space.

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David Dumas, Michael Wolf. 2015-09-24. Polynomial cubic differentials and convex polygons in the projective plane. https://arxiv.org/abs/1407.8149

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