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arxiv: 2606.06733 · v1 · pith:5CEAEVQ2new · submitted 2026-06-04 · 🧮 math.AG · hep-th· math-ph· math.MP

Compactified supermoduli space is almost never projected

classification 🧮 math.AG hep-thmath-phmath.MP
keywords compactifiedgenuscomponenteverynon-projectedsupermodulialmostcomponents
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We settle the projectedness problem for the compactified unpunctured supermoduli stack in every genus at least two. In genus two, the odd component is split, whereas the even component is non-projected. In every genus $g\geq 3$, both compactified parity components are non-projected.

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