Finite translation surfaces with maximal number of translations

Jan-Christoph Schlage-Puchta; Gabriela Weitze-Schmithuesen

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arXiv · 1311.7446

Finite translation surfaces with maximal number of translations

Jan-Christoph Schlage-Puchta·Gabriela Weitze-Schmithuesen

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Abstract

The natural automorphism group of a translation surface is its group of translations. For finite translation surfaces of genus g > 1 the order of this group is naturally bounded in terms of g due to a Riemann-Hurwitz formula argument. In analogy with classical Hurwitz surfaces, we call surfaces which achieve the maximal bound Hurwitz translation surfaces. We study for which g there exist Hurwitz translation surfaces of genus g.

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BibTeX RIS

Jan-Christoph Schlage-Puchta, Gabriela Weitze-Schmithuesen. 2013-11-28. Finite translation surfaces with maximal number of translations. https://arxiv.org/abs/1311.7446

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