The McKay Correspondence for Dihedral Groups: The Moduli Space and the Tautological Bundles
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929732025581568 |
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| author | Capellan, John Ashley Navarro |
| author_facet | Capellan, John Ashley Navarro |
| contents | A conjecture in [Ish20] states that for a finite subgroup $G$ of $GL(2; \mathbb{C})$, a resolution $Y$ of $\mathbb{C}^2/G$ is isomorphic to a moduli space $\mathcal{M}_θ$ of $G$-constellations for some generic stability parameter $θ$ if and only if $Y$ is dominated by the maximal resolution. This paper affirms the conjecture in the case of dihedral groups as a class of complex reflection groups, and offers an extension of McKay correspondence (via [IN1], [IN2], and [Ish02]). To appear in Hiroshima Mathematical Journal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09491 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The McKay Correspondence for Dihedral Groups: The Moduli Space and the Tautological Bundles Capellan, John Ashley Navarro Algebraic Geometry Representation Theory 14D20, 14E16, 14J17 A conjecture in [Ish20] states that for a finite subgroup $G$ of $GL(2; \mathbb{C})$, a resolution $Y$ of $\mathbb{C}^2/G$ is isomorphic to a moduli space $\mathcal{M}_θ$ of $G$-constellations for some generic stability parameter $θ$ if and only if $Y$ is dominated by the maximal resolution. This paper affirms the conjecture in the case of dihedral groups as a class of complex reflection groups, and offers an extension of McKay correspondence (via [IN1], [IN2], and [Ish02]). To appear in Hiroshima Mathematical Journal. |
| title | The McKay Correspondence for Dihedral Groups: The Moduli Space and the Tautological Bundles |
| topic | Algebraic Geometry Representation Theory 14D20, 14E16, 14J17 |
| url | https://arxiv.org/abs/2405.09491 |