# Decorated Marked Surfaces III: The Derived Category of a Decorated Marked Surface

@article{Buan2019DecoratedMS, title={Decorated Marked Surfaces III: The Derived Category of a Decorated Marked Surface}, author={Aslak Bakke Buan and Yu Qiu and Yu Zhou}, journal={International Mathematics Research Notices}, year={2019} }

We study the Ginzburg dg algebra $\Gamma _{\mathbf {T}}$ associated with the quiver with potential arising from a triangulation $\mathbf {T}$ of a decorated marked surface ${\mathbf {S}}_\bigtriangleup$, in the sense of [22]. We show that there is a canonical way to identify all finite-dimensional derived categories $\operatorname {\mathcal {D}}_{fd}(\Gamma _{\mathbf {T}})$, denoted by $\operatorname {\mathcal {D}}_{fd}({\mathbf {S}}_\bigtriangleup )$. As an application, we show that the… Expand

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