A counterexample to the Jordan-H\"older property for polarizable semiorthogonal decompositions
Representation Theory
2025-03-10 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2502.12075,
title = {A counterexample to the Jordan-H\"older property for polarizable semiorthogonal decompositions},
author = {Fabian Haiden and Dongjian Wu},
journal= {arXiv preprint arXiv:2502.12075},
year = {2025}
}
Comments
v2: references added