Veech Groups and Translation Coverings

Beschreibung

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.
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.

Autor*in

Myriam Finster

Themen in »Veech Groups and Translation Coverings«

Translationsüberlagerung Monodromiegruppe Kongruenzgruppe monodromy group Veech group congruence subgroup cyclic covering zyklische Überlagerung translation covering Veechgruppe

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