Full Exceptional Sequence for a Fine Quiver Moduli Space
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912162779234304 |
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| author | Makarova, Svetlana Meng, Junyu |
| author_facet | Makarova, Svetlana Meng, Junyu |
| contents | We consider the fine quiver moduli space of representations of the 3-Kronecker quiver of dimension vector $(2,3)$, which is a blow down of the Hilbert scheme of 3 points on $\mathds{P}^2$. A short description of its geometry and Chow ring is given. Then we exhibit an exceptional sequence for the derived category by understanding a $\mathds{P}^1$-bundle over it and using Teleman Quantization. The fullness of the exceptional sequence is proved by using a covering argument and computations of mutations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_15390 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Full Exceptional Sequence for a Fine Quiver Moduli Space Makarova, Svetlana Meng, Junyu Algebraic Geometry We consider the fine quiver moduli space of representations of the 3-Kronecker quiver of dimension vector $(2,3)$, which is a blow down of the Hilbert scheme of 3 points on $\mathds{P}^2$. A short description of its geometry and Chow ring is given. Then we exhibit an exceptional sequence for the derived category by understanding a $\mathds{P}^1$-bundle over it and using Teleman Quantization. The fullness of the exceptional sequence is proved by using a covering argument and computations of mutations. |
| title | Full Exceptional Sequence for a Fine Quiver Moduli Space |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.15390 |