Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Wang, Jianping, Zhang, Xucheng
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221772372