Fusion-equivariant stability conditions and Morita duality

Fusion-equivariant stability conditions and Morita duality

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 modu...

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Veröffentlicht in:arXiv.org 2024-03
Hauptverfasser: Dell, Hannah, Heng, Edmund, Licata, Anthony M
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Manifolds (mathematics)
Stability
Topology
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description 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, we generalise a result of Macr\`{i}--Mehrotra--Stellari by establishing a homeomorphism 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.
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title Fusion-equivariant stability conditions and Morita duality
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