• Citer

Comparing the Kirwan and noncommutative resolutions of quotient varieties

par Spenko, Špela ;Van den Bergh, Michel
Référence Journal für die reine und angewandte Mathematik, 0, 0
Publication Publié, 2023-07-01

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

Abstract Let a reductive group G act on a smooth variety X such that a good quotient X / / G {X/!!/G} exists. We show thatthe derived category of a noncommutative crepant resolution (NCCR) of X / / G {X/!!/G} , obtained from a G -equivariant vector bundle on X ,can be embedded in thederived category of the (canonical, stacky) Kirwan resolution of X / / G {X/!!/G} .In fact, the embedding can be completed to a semi-orthogonal decomposition in which the other partsare all derived categories of Azumaya algebras over smooth Deligne–Mumford stacks.