Algebraicity of supermoduli of curves via Artin's criteria

TL;DR

This paper proves the algebraicity of various supermoduli spaces, including supercurves and super Riemann surfaces, using supergeometric Artin's criteria, providing new proofs and results in supergeometry.

Contribution

It introduces a supergeometric version of Artin's algebraicity criteria and applies it to establish the algebraicity of moduli of supercurves and stable supercurves, with new proofs for some cases.

Findings

Algebraicity of moduli of supercurves established for the first time.

New proof of algebraicity for moduli of super Riemann surfaces.

Verification of super Artin conditions for these moduli spaces.

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.