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

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1804.00094
 Bibcode:
 2018arXiv180400094B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Rings and Algebras
 EPrint:
 20 pages, comments are welcome