Schemes of modules over gentle algebras and laminations of surfaces

I will speak about some geometric aspects of the representation theory of gentle algebras. Some results regarding the irreducible components of the affine schemes of modules over gentle algebras will be presented. In the case of gentle algebras arising from triangulations of unpunctured surfaces, a bijection between the set of laminations on the surface and the set of generically \(\tau\)-reduced irreducible components (formerly called “strongly reduced” by Geiss–Leclerc–Schröer) will be described. The talk is based on joint work with Christof Geiss and Jan Schröer.