Stability scattering diagrams and quiver coverings
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916993837301760 |
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| author | Chen, Qiyue Mandel, Travis Qin, Fan |
| author_facet | Chen, Qiyue Mandel, Travis Qin, Fan |
| contents | Given a covering of a quiver (with potential), we show that the associated Bridgeland stability scattering diagrams are related by a restriction operation under the assumption of admitting a nice grading. We apply this to quivers with potential associated to marked surfaces. In combination with recent results of the second and third authors, our findings imply that the bracelets basis for a once-punctured closed surface coincides with the theta basis for the associated stability scattering diagram, and these stability scattering diagrams agree with the corresponding cluster scattering diagrams of Gross-Hacking-Keel-Kontsevich except in the case of the once-punctured torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_04104 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability scattering diagrams and quiver coverings Chen, Qiyue Mandel, Travis Qin, Fan Representation Theory Algebraic Geometry General Topology 13F60 Given a covering of a quiver (with potential), we show that the associated Bridgeland stability scattering diagrams are related by a restriction operation under the assumption of admitting a nice grading. We apply this to quivers with potential associated to marked surfaces. In combination with recent results of the second and third authors, our findings imply that the bracelets basis for a once-punctured closed surface coincides with the theta basis for the associated stability scattering diagram, and these stability scattering diagrams agree with the corresponding cluster scattering diagrams of Gross-Hacking-Keel-Kontsevich except in the case of the once-punctured torus. |
| title | Stability scattering diagrams and quiver coverings |
| topic | Representation Theory Algebraic Geometry General Topology 13F60 |
| url | https://arxiv.org/abs/2306.04104 |