Year: 2025
Type: article
Abstract: Given a triangulated category $${\mathcal {D}}$$ D with an action of a fusion category $${\mathcal {C}}$$ C , we study the moduli space $${{\,\textrm{Stab}\,}}_{{\mathcal {C}}}({\mathcal {D}})$$ Stab C ( D ) of fusion-equivariant Bridgeland stability conditions on $${\mathcal {D}}$$ D . The main theorem is that the fusion-equivariant stability conditions form a closed, complex submanifold of the moduli space of stability conditions on $${\mathcal {D}}$$ 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 $${\mathcal {D}}$$ D and the space of $${\textsf{rep}}(G)$$ rep ( G ) -equivariant stability conditions on the equivariant category $${\mathcal {D}}^G$$ 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.
Source: Mathematische Zeitschrift
Authors: Hannah Dell, Edmund Heng, Anthony M. Licata
Institutions: University of Bonn, Maxwell Institute for Mathematical Sciences, University of Edinburgh, The University of Sydney, Institut des Hautes Études Scientifiques, Australian National University, Centre National de la Recherche Scientifique, France Australia Mathematical Sciences and Interactions International Research Lab
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4414001824