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arXiv · 1804.00094

Decorated marked surfaces III: The derived category of a decorated marked surface

Aslak Bakke Buan·Yu Qiu·Yu Zhou
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Abstract

We study the Ginzburg dg algebra $\Gamma_\mathbf{T}$ associated to the quiver with potential arising from a triangulation $\mathbf{T}$ of a decorated marked surface $\mathbf{S}_\bigtriangleup$, in the sense of Qiu. We show that there is a canonical way to identify all finite dimensional derived categories $\mathcal{D}_{fd}(\Gamma_\mathbf{T})$, denoted by $\mathcal{D}_{fd}(\mathbf{S}_\bigtriangleup)$. As an application, we show that the spherical twist group $\operatorname{ST}(\mathbf{S}_\bigtriangleup)$ associated to $\mathcal{D}_{fd}(\mathbf{S}_\bigtriangleup)$ acts faithfully on its space of stability conditions.

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Aslak Bakke Buan, Yu Qiu, Yu Zhou. 2018-03-31. Decorated marked surfaces III: The derived category of a decorated marked surface. https://arxiv.org/abs/1804.00094

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