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arXiv · 2412.04777

A space of stability conditions that is not a length space

Yu-Wei Fan
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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.

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Yu-Wei Fan. 2024-12-06. A space of stability conditions that is not a length space. https://arxiv.org/abs/2412.04777

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