Algebraicity of supermoduli of curves via Artin's criteria

Abstract

We apply the supergeometric analogue of Artin's algebraicity criteria to prove algebraicity for four moduli problems in supergeometry: supercurves, super Riemann surfaces, stable supercurves, and stable super Riemann surfaces. The algebraicity of the moduli of (stable) super Riemann surfaces is known but we give a new proof by verifying the super Artin conditions. The algebraicity of the moduli of (stable) supercurves is new.