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Existence of moduli spaces for algebraic stacks

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arxiv 1812.01128 v5 pith:LTDUXUWN submitted 2018-12-03 math.AG

Jarod Alper , Daniel Halpern-Leistner , Jochen Heinloth This is my paper · ORCID
classification math.AG
keywords modulialgebraicspacesgoodobjectsproperresultssemistable
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abstract

We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. These results provide a generalization of the Keel--Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem to have a separated or proper good moduli space. To illustrate our method, we apply these results to construct proper moduli spaces parameterizing semistable $\mathcal{G}$-bundles on curves and moduli spaces for objects in abelian categories.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The hyper-Kummer construction

    math.AG 2026-07 accept novelty 8.0 of 10

    A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.

  2. Proper moduli spaces of orthosymplectic complexes

    math.AG 2025-12 conditional novelty 7.0 of 10

    Semistable orthosymplectic complexes on smooth projective varieties admit proper good moduli spaces, giving a new compactification for O_n and Sp_{2n} principal bundle moduli.

  3. On the Feyzbakhsh-Thomas programme for Fano $3$-folds

    math.AG 2026-07 conditional novelty 6.0 of 10

    For Fano 3-folds with even canonical class and a generalized Bogomolov-Gieseker inequality, rank r Donaldson-Thomas invariants are universally determined by rank 0, pure dimension 2 invariants.

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