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A counterexample to the Jordan-H\"older property for polarizable semiorthogonal decompositions

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arxiv 2502.12075 v2 pith:M5YSL7T5 submitted 2025-02-17 math.RT math.AG

Fabian Haiden , Dongjian Wu This is my paper · ORCID
classification math.RTmath.AG
keywords categoriesconditiondecompositionsjordan-holderpolarizablepropertysemiorthogonal
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We show that the Jordan-H\"older property fails for polarizable semiorthogonal decompositions -- those where every factor admits a Bridgeland stability condition. Counterexamples exist among Fukaya categories of surfaces and bounded derived categories of smooth projective varieties. Furthermore, we give an example of a smooth and proper pre-triangulated dg category with positive rank Grothendieck group which does not admit a stability condition.

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  1. A Real Reduction of the Manifold of Bridgeland Stability Conditions

    math.AG 2025-06 accept novelty 7.0 of 10

    A quotient of the stability manifold by an equivalence relation is a real manifold of half dimension, and the original manifold can be reconstructed from the quotient together with the relation ≲.

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