Ishii's conjecture and Bridgeland stability conditions for dihedral reflection groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911704680497152 |
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| author | Nimura, Shu |
| author_facet | Nimura, Shu |
| contents | We provide a new proof of Ishii's conjecture for any dihedral reflection group $G\subset GL_2(\mathbb{C})$ from the viewpoint of Bridgeland stability conditions. Our strategy is to reduce the problem, via the derived McKay correspondence, to a geometric construction of Bridgeland stability conditions on the root stack of the maximal resolution along the strict transform of the discriminant divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22474 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ishii's conjecture and Bridgeland stability conditions for dihedral reflection groups Nimura, Shu Algebraic Geometry We provide a new proof of Ishii's conjecture for any dihedral reflection group $G\subset GL_2(\mathbb{C})$ from the viewpoint of Bridgeland stability conditions. Our strategy is to reduce the problem, via the derived McKay correspondence, to a geometric construction of Bridgeland stability conditions on the root stack of the maximal resolution along the strict transform of the discriminant divisor. |
| title | Ishii's conjecture and Bridgeland stability conditions for dihedral reflection groups |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.22474 |