Graded Riemann surfaces
What super Riemann surfaces should be is a fundamental question in the theory of superstrings. There has been a lot of activity for describing super Riemann surfaces and the super Teichmüller spaces that classify them. Most descriptions use a subcategory of \(G^{\infty}\)- supermanifolds in which the coordinate charts have a simple form (de Witt manifolds). This paper considers the more restrictive case of Riemann surfaces in the category of graded manifolds. The authors think that the gain in doing this is the evident role of the double cover Sl(2,C) of the Lorentz group in the classification of graded Riemann surfaces. The results are as follows: 1. The group Sl(2,C) plays the role of the Möbius group as the automorphism group of the algebra of graded rational functions. 2. All graded Riemann surfaces occur as quotients of simply connected graded Riemann surfaces by discrete subgroup of Sl(2,C).
scientific article; zbMATH DE number 4077662
scientific article