Derived Category of certain maximal order on $\mathbb{P}^{2}$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910624421773312 |
|---|---|
| author | Shen, Yu |
| author_facet | Shen, Yu |
| contents | We show that the moduli space of $A$-line bundles with minimal second Chern class is a fine moduli space, where $A$ is a maximal quaternion order on $\mathbb{P}^{2}$ ramified along a smooth quartic. We prove that there is a fully faithful embedding from the derived category of this moduli space into the derived category of $A$-modules. Furthermore, we find a semiorthogonal decomposition for $D^{b}(\mathbb{P}^{2},A)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derived Category of certain maximal order on $\mathbb{P}^{2}$ Shen, Yu Algebraic Geometry Rings and Algebras 14J60, 16H05 We show that the moduli space of $A$-line bundles with minimal second Chern class is a fine moduli space, where $A$ is a maximal quaternion order on $\mathbb{P}^{2}$ ramified along a smooth quartic. We prove that there is a fully faithful embedding from the derived category of this moduli space into the derived category of $A$-modules. Furthermore, we find a semiorthogonal decomposition for $D^{b}(\mathbb{P}^{2},A)$. |
| title | Derived Category of certain maximal order on $\mathbb{P}^{2}$ |
| topic | Algebraic Geometry Rings and Algebras 14J60, 16H05 |
| url | https://arxiv.org/abs/2409.19857 |