Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces

• Verfasst von: Beckmann, Thorsten [VerfasserIn]
• Verfasst von: Oberdieck, Georg [VerfasserIn]
• Titel: Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces
• Verf.angabe: Thorsten Beckmann and Georg Oberdieck
• Jahr: 2022
• Umfang: 43 S.
• Fussnoten: Gesehen am 12.12.2024
• Titel Quelle: Enthalten in: Algebraic geometry
• Ort Quelle: Amsterdam, The Netherlands : Foundation Compositio Mathematica, 2014
• Jahr Quelle: 2022
• Band/Heft Quelle: 9(2022), 4, Seite 400-442
• ISSN Quelle: 2313-1691
• DOI: doi:10.14231/AG-2022-012
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1912167042

Abstract

Given an action of a finite group G on the derived category of a smooth projective variety X, we relate the fixed loci of the induced G-action on moduli spaces of stable objects in Db(Coh(X)) with moduli spaces of stable objects in the equivariant category Db(Coh(X))G. As an application, we obtain a criterion for the equivariant category of a symplectic action on the derived category of a symplectic surface to be equivalent to the derived category of a surface. This generalizes the derived McKay correspondence and yields a general framework for describing fixed loci of symplectic group actions on moduli spaces of stable objects on symplectic surfaces.