English

Effective morphisms and quotient stacks

Algebraic Geometry 2024-01-29 v2

Abstract

We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective morphisms, which are a generalization of separated morphisms.

Keywords

Cite

@article{arxiv.2303.10751,
  title  = {Effective morphisms and quotient stacks},
  author = {Andrea Di Lorenzo and Giovanni Inchiostro},
  journal= {arXiv preprint arXiv:2303.10751},
  year   = {2024}
}

Comments

25 pages, comments are welcome! v2: we corrected a gap in a proof and slightly modified the definition of effective morphism. To appear on IMRN

R2 v1 2026-06-28T09:23:07.247Z