Fusion-equivariant stability conditions and Morita duality
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908475879063552 |
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| author | Dell, Hannah Heng, Edmund Licata, Anthony M. |
| author_facet | Dell, Hannah Heng, Edmund Licata, Anthony M. |
| contents | Given a triangulated category $D$ with an action of a fusion category $C$, we study the moduli space $Stab_{C}(D)$ of fusion-equivariant Bridgeland stability conditions on $D$. The main theorem is that the fusion-equivariant stability conditions form a closed, complex submanifold of the moduli space of stability conditions on $D$. As an application of this framework to finite group actions on categories, we generalise a result of Macrì--Mehrotra--Stellari by establishing a biholomorphism between the space of $G$-invariant stability conditions on $D$ and the space of $rep(G)$-equivariant stability conditions on the equivariant category $D^G$. We also describe applications to the study of stability conditions associated to McKay quivers and to geometric stability conditions on free quotients of smooth projective varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06857 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fusion-equivariant stability conditions and Morita duality Dell, Hannah Heng, Edmund Licata, Anthony M. Representation Theory Algebraic Geometry Quantum Algebra 18M20 (Primary), 16G20, 14F08, 14L30 (Secondary) Given a triangulated category $D$ with an action of a fusion category $C$, we study the moduli space $Stab_{C}(D)$ of fusion-equivariant Bridgeland stability conditions on $D$. The main theorem is that the fusion-equivariant stability conditions form a closed, complex submanifold of the moduli space of stability conditions on $D$. As an application of this framework to finite group actions on categories, we generalise a result of Macrì--Mehrotra--Stellari by establishing a biholomorphism between the space of $G$-invariant stability conditions on $D$ and the space of $rep(G)$-equivariant stability conditions on the equivariant category $D^G$. We also describe applications to the study of stability conditions associated to McKay quivers and to geometric stability conditions on free quotients of smooth projective varieties. |
| title | Fusion-equivariant stability conditions and Morita duality |
| topic | Representation Theory Algebraic Geometry Quantum Algebra 18M20 (Primary), 16G20, 14F08, 14L30 (Secondary) |
| url | https://arxiv.org/abs/2311.06857 |