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

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

19 pages