Moduli of $G$-constellations and crepant resolutions II: the Craw-Ishii conjecture
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909174851436544 |
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| author | Yamagishi, Ryo |
| author_facet | Yamagishi, Ryo |
| contents | For any given finite subgroup $G\subset SL_3(\mathbb{C})$, we show that every projective crepant resolution $X$ of the quotient variety $\mathbb{C}^3/G$ is isomorphic to the moduli space of $θ$-stable $G$-constellations for a generic stability condition $θ$, as conjectured by Craw and Ishii. We also show that generators of the Cox ring of $X$ can be obtained from semi-invariants for representations of the McKay quiver of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_11901 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Moduli of $G$-constellations and crepant resolutions II: the Craw-Ishii conjecture Yamagishi, Ryo Algebraic Geometry For any given finite subgroup $G\subset SL_3(\mathbb{C})$, we show that every projective crepant resolution $X$ of the quotient variety $\mathbb{C}^3/G$ is isomorphic to the moduli space of $θ$-stable $G$-constellations for a generic stability condition $θ$, as conjectured by Craw and Ishii. We also show that generators of the Cox ring of $X$ can be obtained from semi-invariants for representations of the McKay quiver of $G$. |
| title | Moduli of $G$-constellations and crepant resolutions II: the Craw-Ishii conjecture |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2209.11901 |