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arXiv · 2610.08742

The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings

Luca Battistella·Andrea Di Lorenzo·Michele Pernice
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Abstract

We classify all open substacks admitting a proper good moduli space inside the stack $\mathcal{G}_{1,n}$ of log-canonically polarized Gorenstein curves of genus one with $n$ distinct marked points: they are exactly the stacks $\overline{\mathcal{M}}_{1,n}(c)$ defined by Bozlee--Kuo--Neff. Restricting to the case where $c$ is pure of level $m$, we then give a numerical criterion for the projectivity of the good moduli spaces: these turn out to be asymptotically almost never projective as $n$ tends to infinity.

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Luca Battistella, Andrea Di Lorenzo, Michele Pernice. 2026-10-06. The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings. https://arxiv.org/abs/2610.08742

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