Functorial destackification of tame stacks with abelian stabilisers

DOI10.1112/S0010437X17007084zbMath1372.14002arXiv1409.5713MaRDI QIDQ5274774

Daniel Bergh

Publication date: 6 July 2017

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5713

zbMATH Keywords

desingularizationalgebraic stacktame stackdestackificatonfunctorial divisorialificationindependency indexstacky blow-up sequencestacky blow-upstoroidal indextoroidal stacks

Mathematics Subject Classification ID

Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Rational and birational maps (14E05) Generalizations (algebraic spaces, stacks) (14A20)

Related Items (18)

Weak factorization and the Grothendieck group of Deligne-Mumford stacks ⋮ Destackification with restricted root operations ⋮ Equivariant birational types and Burnside volume ⋮ The Nori fundamental gerbe of tame stacks ⋮ Birational invariants of toric orbifold surfaces ⋮ Toroidal orbifolds, destackification, and Kummer blowings up ⋮ Principalization of ideals on toroidal orbifolds ⋮ Equivariant Hodge theory and noncommutative geometry ⋮ Fundamental gerbes ⋮ Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties ⋮ \(K\)-theory and the singularity category of quotient singularities ⋮ Maps of Mori dream spaces ⋮ Conic bundles and iterated root stacks ⋮ Geometricity for derived categories of algebraic stacks ⋮ Canonical reduction of stabilizers for Artin stacks with good moduli spaces ⋮ Birational types of algebraic orbifolds ⋮ On the spaces generated by vectors with coordinates in incomplete residue systems ⋮ Categorical measures for finite group actions

Cites Work

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• The Chevalley-Shephard-Todd theorem for finite linearly reductive group schemes
• Quotients by groupoids
• Partial desingularizations of good moduli spaces of Artin toric stacks
• Étale dévissage, descent and pushouts of stacks
• Toroidal embeddings. I
• Logarithmic geometry, minimal free resolutions and toric algebraic stacks
• Intersection theory on algebraic stacks and on their moduli spaces
• Tame stacks in positive characteristic
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• Kawamata-Viehweg vanishing as Kodaira vanishing for stacks
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Existence and properties of geometric quotients
• Smooth toric Deligne-Mumford stacks
• Equivariant Embeddings into Smooth Toric Varieties
• The orbifold Chow ring of toric Deligne-Mumford stacks
• Lectures on Resolution of Singularities (AM-166)
• Using stacks to impose tangency conditions on curves
• Gromov-Witten theory of Deligne-Mumford stacks
• The category of toric stacks
• Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties
• Tensor generators on schemes and stacks
• Toric stacks I: The theory of stacky fans
• Toric stacks II: Intrinsic characterization of toric stacks

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