Hyperbolic geometry and moduli of real curves of genus three

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...

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Published in:Mathematische annalen 2018-04, Vol.370 (3-4), p.1321-1360
Main Authors: Heckman, Gert, Rieken, Sander
Format: Article
Language:English
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Curves
Geometry
Integers
Mathematics
Mathematics and Statistics
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description 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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subjects Curves
Geometry
Integers
Mathematics
Mathematics and Statistics
title Hyperbolic geometry and moduli of real curves of genus three
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