تقرير
Fusion-equivariant stability conditions and Morita duality
| العنوان: | Fusion-equivariant stability conditions and Morita duality |
|---|---|
| المؤلفون: | Dell, Hannah, Heng, Edmund, Licata, Anthony M. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Algebraic Geometry, Mathematics - Quantum Algebra, 18M20 (Primary), 16G20, 14F08, 14L30 (Secondary) |
| الوصف: | 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. Comment: v2: Updated the proof of lemma 3.17 (3.16 in previous version); new geometrical applications included; added an appendix dealing with the support property. v1: 30 pages. Comments more than welcomed! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.06857 |
| رقم الأكسشن: | edsarx.2311.06857 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |