A space of stability conditions that is not a length space
Algebraic Geometry
2025-06-10 v2 Metric Geometry
Abstract
We prove that the space of Bridgeland stability conditions, when equipped with the canonical metric, is not a length space in general. This resolves a question posed by Kikuta in the negative. Furthermore, we introduce two modified metrics on the stability spaces, which may exhibit better metric properties.
Keywords
Cite
@article{arxiv.2412.04777,
title = {A space of stability conditions that is not a length space},
author = {Yu-Wei Fan},
journal= {arXiv preprint arXiv:2412.04777},
year = {2025}
}