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Relative Stability Conditions on Triangulated Categories

Published 3 Nov 2024 in math.AG, math.CT, and math.DG | (2411.01502v3)

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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