Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces
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 c...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2022
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| In: |
Algebraic geometry
Year: 2022, Jahrgang: 9, Heft: 4, Pages: 400-442 |
| ISSN: | 2313-1691 |
| DOI: | 10.14231/AG-2022-012 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.14231/AG-2022-012 Verlag, lizenzpflichtig, Volltext: http://content.algebraicgeometry.nl/2022-4/2022-4-012.pdf 
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| Verfasserangaben: | Thorsten Beckmann and Georg Oberdieck |
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| 520 | |a 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. | ||
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