Graded decorated marked surfaces: Calabi-Yau-$\mathbb{X}$ categories of gentle algebras

Akishi Ikeda, Yu Qiu, Yu Zhou

Let $\mathbf{S}$ be a graded marked surface. We construct a string model for Calabi-Yau-$\mathbb{X}$ category ${\mathcal{D}}_{\mathbb{X}}({\mathbf{S}}_{△})$, via the graded DM…