Special K\"ahler structures, cubic differentials and hyperbolic metrics
Differential Geometry
2020-03-11 v2 Algebraic Geometry
Abstract
We obtain necessary conditions for the existence of special K\"ahler structures with isolated singularities on compact Riemann surfaces. We prove that these conditions are also sufficient in the case of the Riemann sphere and, moreover, we determine the whole moduli space of special K\"ahler structures with fixed singularities. The tool we develop for this aim is a correspondence between special K\"ahler structures and pairs consisting of a cubic differential and a hyperbolic metric.
Cite
@article{arxiv.1807.08550,
title = {Special K\"ahler structures, cubic differentials and hyperbolic metrics},
author = {Andriy Haydys and Bin Xu},
journal= {arXiv preprint arXiv:1807.08550},
year = {2020}
}
Comments
v2: Results strengthened, added a section on compactifications of the moduli spaces, exposition improved