Compactified supermoduli stack is non-projected for g>=3 (both parity components) and for the even component in g=2; odd component in g=2 is split.
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Compactified supermoduli space is almost never projected
Compactified supermoduli stack is non-projected for g>=3 (both parity components) and for the even component in g=2; odd component in g=2 is split.