Deforming super Riemann surfaces with gravitinos and super Schottky groups

Abstract

The (super) Schottky uniformization of compact (super) Riemann surfaces is briefly reviewed. Deformations of super Riemann surface by gravitinos and Beltrami parameters are recast in terms of super Schottky group cohomology. It is checked that the super Schottky group formula for the period matrix of a non-split surface matches its expression in terms of a gravitino and Beltrami parameter on a split surface. The relationship between (super) Schottky groups and the construction of surfaces by gluing pairs of punctures is discussed in an appendix.