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...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische annalen 2018-04, Vol.370 (3-4), p.1321-1360
Main Authors: Heckman, Gert, Rieken, Sander
Format: Article
Language:English
Subjects:
Curves
Geometry
Integers
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-017-1587-2