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arXiv · 2610.15831

Open substacks preserving moduli spaces: classification and bounds

Jianping Wang·Xucheng Zhang
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Abstract

For a smooth locally reductive stack admitting an adequate moduli space, we show that there are finitely many open substacks preserving the adequate moduli space, and give a complete classification of such opens. For $\mathbb{G}_m$-actions, this becomes an explicit description in terms of the codimension-one Bialynicki-Birula strata. Moreover, for a stable adequate moduli space, we show that the number of preserving opens are bounded by 3 raised to the relative Picard rank. As an application, the number of fixed components for $\mathbb{G}_m$-actions is at least the relative Picard rank.

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Jianping Wang, Xucheng Zhang. 2026-10-11. Open substacks preserving moduli spaces: classification and bounds. https://arxiv.org/abs/2610.15831

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