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Veech Groups and Translation Coverings
Finster, Myriam
2014
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A translation surface is obtained by taking plane polygons and gluing their edges by translations. We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering. For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface. We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.
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Keywords
- congruence subgroup
- cyclic covering
- Kongruenzgruppe
- Monodromiegruppe
- monodromy group
- translation coveringVeechgruppe
- Translationsüberlagerung
- Veech group
- zyklische Überlagerung
Links
DOI: 10.5445/KSP/1000038927Editions