Graded Riemann surfaces

Abstract

There has been a lot of activity directed at describing super Riemann surfaces and the super Teichmuller spaces that classify them. Most descriptions use a subcategory ofG∞-supermanifolds in which the coordinate charts have a particularly simple form (“de Witt” supermanifolds). This paper considers the more restrictive case of Riemann surfaces in the category of graded manifolds. The gain in doing this is the evident role of the double coverSl(2,C) of the Lorentz group in the classification of graded Riemann surfaces.