Special vs Essential
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913028524474368 |
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| author | Ito, Yukari Sato, Kohei Sato, Yusuke |
| author_facet | Ito, Yukari Sato, Kohei Sato, Yusuke |
| contents | We show a correspondence between the compact exceptional curves and divisors on $G-{\rm Hilb}(\mathbf{C}^3)$ and some non-trivial irreducible representations of $G \subset GL(n,C)$ which are special (or essential). Moreover, we provide an explicit construction of the small resolution of $G-{\rm Hilb}(\mathbf{C}^3)$ and, using this resolution, we construct a correspondence between special and essential representations. These results are an extension of ``Special McKay correspondence'' and ``Reid's recipe''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05634 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Special vs Essential Ito, Yukari Sato, Kohei Sato, Yusuke Algebraic Geometry We show a correspondence between the compact exceptional curves and divisors on $G-{\rm Hilb}(\mathbf{C}^3)$ and some non-trivial irreducible representations of $G \subset GL(n,C)$ which are special (or essential). Moreover, we provide an explicit construction of the small resolution of $G-{\rm Hilb}(\mathbf{C}^3)$ and, using this resolution, we construct a correspondence between special and essential representations. These results are an extension of ``Special McKay correspondence'' and ``Reid's recipe''. |
| title | Special vs Essential |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.05634 |