A space of stability conditions that is not a length space
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916782581743616 |
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| author | Fan, Yu-Wei |
| author_facet | Fan, Yu-Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A space of stability conditions that is not a length space Fan, Yu-Wei Algebraic Geometry Metric Geometry 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. |
| title | A space of stability conditions that is not a length space |
| topic | Algebraic Geometry Metric Geometry |
| url | https://arxiv.org/abs/2412.04777 |