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Gabriela Weitze-Schmithuesen

Publications and source records attributed to Gabriela Weitze-Schmithuesen.

5 recordsLinked to original sources
arXiv2018

Totally non congruence Veech groups

Veech groups are discrete subgroups of SL(2, R) which play an important role in the theory of translation surfaces. For a special class of translation surfaces called origamis or square-tiled surfaces their Veech groups are subgroups of finite index of SL(2, Z). We show that each stratum of the space of translation surfaces contains infinitely many origamis whose Veech group is a totally non congruence group, i.e. it surjects to SL(2, Z/nZ) for any n.

math.GT↗
arXiv2013

Finite translation surfaces with maximal number of translations

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.

math.GT↗
arXiv2013

On the geometry and arithmetic of infinite translation surfaces

There are only a few invariants one classically associates with precompact translation surfaces, among them certain numberfields, i.e. fields which are finite extensions of the field Q of rational numbers. These fields are closely related to each other; they are often even equal. We prove by constructing explicit examples that most of the classical results for number fields associated to precompact translation surfaces fail in the realm of general translation surfaces and investigate the relations among these fields. A very special class of translation surfaces are so called square-tiled surfaces or origamis. We give a characterization for infinite origamis.

math.DG↗
arXiv2012

The deficiency of being a congruence group for Veech groups of origamis

We study "how far away" a finite index subgroup G of SL(2,Z) is from being a congruence group. For this we define its deficiency of being a congruence group. We show that the index of the image of G in SL(2,Z/nZ) is biggest, if n is the general Wohlfahrt level. We furthermore show that the Veech groups of origamis (or square-tiled surfaces) in the stratum H(2) are far away from being congruence groups and that in each genus one finds an infinite family of origamis such that they are "as far as possible" from being a congruence group.

math.GT↗