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arXiv · 2608.14099

The Hassett-Keel program via $\Theta$-stability

Luca Tasin·Filippo Viviani
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Abstract

We study the intrinsic notion of $\alpha$-stability for curves arising from the Beyond GIT approach to moduli spaces. We show that it recovers Deligne-Mumford stability for $9/11<\alpha\le1$, and more generally that the $\alpha$-semistable locus is contained in the known modular compactification of the Hassett-Keel proram for $\alpha>2/3-\varepsilon$. As applications, we also obtain new $\alpha$-stability results for smooth curves. Our approach combines slope inequalities with a degeneration theorem showing that every Gorenstein curve with a non-nodal singularity can be isotrivially degenerated to a Gorenstein curve with a $\mathbb G_m$-action.

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Luca Tasin, Filippo Viviani. 2026-08-14. The Hassett-Keel program via $\Theta$-stability. https://arxiv.org/abs/2608.14099

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