Super Teichmüller Space

Abstract

The paper contains three results. First, we give a global quotient presentation of the supermoduli space of genus $g>1$ super Riemann surfaces. Second, we prove that the moduli stack of marked super Riemann surfaces, which we call super Teichmüller space, is a complex analytic Deligne Mumford superstack. Third, we construct an étale atlas for super Teichmüller space whose underlying topological space is a disjoint union of $2^{2g}$ contractible unit balls.

arXiv comment30 pages