Abstract

We determine the singularity category of an arbitrary finite dimensional gentle algebra $\Lambda$ . It is a finite product of $n$ -cluster categories of type $\mathbb{A}_{1}$ . Equivalently, it may be described as the stable module category of a selfinjective gentle algebra. If $\Lambda$ is a Jacobian algebra arising from a triangulation ${\mathcal{T}}$ of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of ${\mathcal{T}}$ .