The supermoduli space of genus zero SUSY curves with Ramond punctures

Abstract

We give an explicit quotient construction of the supermoduli space $\mathfrak{M}_{0, n_R}$ of genus zero super Riemann surfaces with $n_R \ge 4$ Ramond punctures and prove it is a Deligne-Mumford superstack. We also make an explicit quotient construction of the moduli space of genus zero supercurves without a SUSY structure and thereby prove it is an algebraic superstack.