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.

Theorems & Definitions (89)

• Theorem 1.1
• Theorem 1.2
• Theorem 1.3
• Proposition 2.1: Proposition A.2, felder2020moduli
• Theorem 2.2
• Definition 3.1
• Lemma 3.2
• proof
• Definition 3.3
• Lemma 3.4