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.
Umfang: X, 136 S.
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Finster, M. 2014. Veech Groups and Translation Coverings. Karlsruhe: KIT Scientific Publishing. DOI: https://doi.org/10.5445/KSP/1000038927
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Veröffentlicht am 26. März 2014