Derived equivalence for the simple flop of type $G_2^{\dagger}$ via tilting bundles
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913071627239424 |
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| author | Hara, Wahei |
| author_facet | Hara, Wahei |
| contents | The aim of this article is to prove the derived equivalence for a local model of the simple flop of type $G_2^{\dagger}$, which was found by Kanemitsu. This flop is the only known simple flop that comes from a non-homogeneous roof. The proof of the derived equivalence is done by using tilting bundles, and also produces a noncommutative crepant resolution of the singularity that is derived equivalent to both sides of the flop. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derived equivalence for the simple flop of type $G_2^{\dagger}$ via tilting bundles Hara, Wahei Algebraic Geometry Rings and Algebras The aim of this article is to prove the derived equivalence for a local model of the simple flop of type $G_2^{\dagger}$, which was found by Kanemitsu. This flop is the only known simple flop that comes from a non-homogeneous roof. The proof of the derived equivalence is done by using tilting bundles, and also produces a noncommutative crepant resolution of the singularity that is derived equivalent to both sides of the flop. |
| title | Derived equivalence for the simple flop of type $G_2^{\dagger}$ via tilting bundles |
| topic | Algebraic Geometry Rings and Algebras |
| url | https://arxiv.org/abs/2412.14314 |