Versal Families of Compact Super Riemann Surfaces

Details Versal Families of Compact Super Riemann Surfaces Versal Families of Compact Super Riemann Surfaces

2011-03-03

arxiv.org/abs/1103.0664v1

Mathematics

Complex Variables

43 pages, no figures

Scientific paper

We call every (1,1)-dimensional super manifold whose body is connected a super Riemann surface and construct versal super families of compact super Riemann surfaces, where the base spaces are allowed to be certain ringed spaces including all complex super manifolds. Furthermore we choose supersymmetric sub super families which turn out to be versal among all supersymmetric super families. In some special cases we prove the non-existence of versal super families and instead construct complete super families. For an accurate study of supersymmetric super families we introduce the duality functor, a covariant involution on the category of super families of compact super Riemann surfaces, and show that the supersymmetric super families are essentially the self-dual ones. As an application of the classification results it is shown that on a supersymmetric super family of compact super Riemann surfaces locally in the base space the supersymmetry is uniquely determined up to pullback by an isomorphism.

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