Polynomial cubic differentials and convex polygons in the projective plane
Differential Geometry
2015-09-28 v3
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.
Cite
@article{arxiv.1407.8149,
title = {Polynomial cubic differentials and convex polygons in the projective plane},
author = {David Dumas and Michael Wolf},
journal= {arXiv preprint arXiv:1407.8149},
year = {2015}
}
Comments
64 pages, 5 figures. v3: Minor revisions according to referee report. v2: Corrections in section 5 and related new material in appendix A