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arXiv · 2409.19857

Derived Category of certain maximal order on $\mathbb{P}^{2}$

Yu Shen
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Abstract

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 $D^{b}(\mathbb{P}^{2},A)$.

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Yu Shen. 2024-09-30. Derived Category of certain maximal order on $\mathbb{P}^{2}$. https://arxiv.org/abs/2409.19857

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