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arXiv · 1612.05785

Hyperbolic Geometry and Moduli of Real Curves of Genus Three

Gert Heckman·Sander Rieken
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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.

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Gert Heckman, Sander Rieken. 2016-12-17. Hyperbolic Geometry and Moduli of Real Curves of Genus Three. https://doi.org/10.1007/s00208-017-1587-2

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