Hyperbolic Geometry and Moduli of Real Curves of Genus Three
Algebraic Geometry
2021-12-14 v1
Abstract
The moduli space of smooth real plane quartic curves consists of six connected components. We prove that each of these components admits a real hyperbolic structure. These connected components correspond to the six real forms of a certain hyperbolic lattice over the Gaussian integers. We will study this Gaussian lattice in detail. For the connected component that corresponds to maximal real quartic curves we obtain a more explicit description. We construct a Coxeter diagram that encodes the geometry of this component.
Keywords
Cite
@article{arxiv.1612.05785,
title = {Hyperbolic Geometry and Moduli of Real Curves of Genus Three},
author = {Gert Heckman and Sander Rieken},
journal= {arXiv preprint arXiv:1612.05785},
year = {2021}
}