Relative Stability Conditions on Triangulated Categories
Bowen Liu, Dongjian Wu
TL;DR
This paper introduces relative stability conditions on triangulated categories, exploring their deformation via gluing stability conditions, motivated by connections to Hermitian-Yang-Mills metrics and Bridgeland stability.
Contribution
It defines a new notion of relative stability conditions with respect to subcategories and studies their deformation properties, extending prior stability frameworks.
Findings
Defined relative stability conditions on triangulated categories.
Demonstrated deformation of these conditions through gluing techniques.
Connected stability conditions to geometric metrics like deformed Hermitian-Yang-Mills.
Abstract
We introduce the notion of relative stability conditions on triangulated categories with respect to left admissible subcategories, based on arXiv:math/0212237, and demonstrate the deformation of relative stability conditions via the deformation of gluing stability conditions in arXiv:0902.0323. The motivation for this concept stems from the discussions in arXiv:2004.04831 concerning the relationship between Bridgeland stability and the existence of the deformed Hermitian-Yang-Mills metrics on line bundles.
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Taxonomy
TopicsRough Sets and Fuzzy Logic · Constraint Satisfaction and Optimization · Topological and Geometric Data Analysis