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Stability functions inducing stability data

  • Fang Li
  • Kangping Qu
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Abstract

In this paper, we study when a stability data on an abelian length category is induced by a stability function. We give an intrinsic characterization of such stability data. For at most six phases, an inducing function exists if and only if every semistable subcategory is wide. An example with seven phases shows that this bound is sharp. For finite phase sets and finite rank, an inducing function exists if and only if an inducing red path exists. We also give a maximal green sequence of length eleven in type D4 that no stability function induces. This disproves the red-path conjecture of Brüstle--Smith--Treffinger.

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Cite

BibTeXRIS
BibTeX
@misc{li2026stability,
  title = {{Stability functions inducing stability data}},
  author = {Fang Li and Kangping Qu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34657},
  eprint = {2610.34657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34657},
}
RIS
TY  - UNPB
TI  - Stability functions inducing stability data
AU  - Fang Li
AU  - Kangping Qu
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34657
UR  - https://arxiv.org/abs/2610.34657
AB  - In this paper, we study when a stability data on an abelian length category is induced by a stability function. We give an intrinsic characterization of such stability data. For at most six phases, an inducing function exists if and only if every semistable subcategory is wide. An example with seven phases shows that this bound is sharp. For finite phase sets and finite rank, an inducing function exists if and only if an inducing red path exists. We also give a maximal green sequence of length eleven in type D_4 that no stability function induces. This disproves the red-path conjecture of Brüstle--Smith--Treffinger.
ER  -