# 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}
}
• Published 31 March 2018
• Mathematics
• International Mathematics Research Notices
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…
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