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arXiv · 2610.00490

Supermoduli spaces are non-projected in every genus $g\geq 3$

Mauricio Corrêa·Ron Donagi·Simone Noja
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Abstract

We prove that, for every genus $g\geq 3$, the primary obstruction of each parity component of the moduli superstack of smooth unpunctured super Riemann surfaces is nonzero, both algebraically and holomorphically. Consequently, both components are non-projected and, in particular, non-split: neither admits an algebraic or holomorphic retraction onto its reduced moduli stack of spin curves.

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Mauricio Corrêa, Ron Donagi, Simone Noja. 2026-09-30. Supermoduli spaces are non-projected in every genus $g\geq 3$. https://arxiv.org/abs/2610.00490

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