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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.01387 |
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| _version_ | 1866917974069215232 |
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| author | Ishii, Akira Nimura, Shu |
| author_facet | Ishii, Akira Nimura, Shu |
| contents | We describe the derived McKay correspondence for real reflection groups of rank $3$ in terms of a maximal resolution of the logarithmic pair consisting of the quotient variety and the discriminant divisor with coefficient $\frac{1}{2}$. As an application, we verify a conjecture by Polishchuk and Van den Bergh on the existence of a certain semiorthgonal decomposition of the equivariant derived category into the derived categories of affine spaces for any real reflection group of rank $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived McKay correspondence for real reflection groups of rank three Ishii, Akira Nimura, Shu Algebraic Geometry We describe the derived McKay correspondence for real reflection groups of rank $3$ in terms of a maximal resolution of the logarithmic pair consisting of the quotient variety and the discriminant divisor with coefficient $\frac{1}{2}$. As an application, we verify a conjecture by Polishchuk and Van den Bergh on the existence of a certain semiorthgonal decomposition of the equivariant derived category into the derived categories of affine spaces for any real reflection group of rank $3$. |
| title | Derived McKay correspondence for real reflection groups of rank three |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.01387 |