A geometric model for the module category of a skew-gentle algebra

Abstract

In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain indecomposable modules, interpret the Auslander-Reiten translation via the tagged rotation, and show intersection-dimension formulas. As an application, we classify support $\ddot{I}„$-tilting modules via maximal collections of non-crossing tagged generalized permissible curves.

Presentation was improved, two tables of notations were added, and a correction for the last condition in the definition of tagged permissible curves was made