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arXiv · 2603.24997

Singularities of Foliations and Good Moduli Spaces of Algebraic Stacks

Federico Bongiorno
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Abstract

Drawing on the theory of Minimal Model Program singularities for foliations, we define relative canonical and log-canonical singularities for algebraic stacks with finite generic stabilisers. We show that if a point has log-canonical singularities, its stabiliser group is a finite extension of an algebraic torus, thus, \'etale locally, the good moduli space exists. If the singularity is canonical, we further show that the locus of stable points is non-empty.

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Federico Bongiorno. 2026-03-26. Singularities of Foliations and Good Moduli Spaces of Algebraic Stacks. https://arxiv.org/abs/2603.24997

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