Singularity categories of gentle algebras

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 $\ct$ of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of $\ct$.

11 pages; minor changes, final version, to appear Bulletin of the LMS

References in corpus (2)

• On triangulated orbit categories
• Derived equivalence classification of m-cluster tilted algebras of type A

Cited by in corpus (24)

• Almost gentle algebras and their trivial extensions
• On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems
• On extensions for gentle algebras
• Singularity categories of Gorenstein monomial algebras
• Mapping cones in the bounded derived category of a gentle algebra
• Singularity categories of representations of algebras over local rings
• Singularity categories of deformations of Kleinian singularities
• The Gorenstein-projective modules over a monomial algebra
• Gentle $m$-Calabi-Yau tilted algebras
• The singularity category of a quadratic monomial algebra
• Cohen-Macaulay Auslander algebras of gentle algebras
• On Cohen-Macaulay Auslander algebras
• Functorial filtrations for homotopy categories of some generalisations of gentle algebras
• On Universal Deformation Rings for Gorenstein Algebras
• Singularity categories of skewed-gentle algebras
• Higher gentle algebras
• Gorenstein defect categories of triangular matrix algebras
• Normed modules, integral sequences, and integrals with variable upper limits
• When stable Cohen-Macaulay Auslander algebra is semisimple
• Desingularization of quiver Grassmannians for Gentle algebras
• The singularity categories of the Cluster-tilted algebras of Dynkin type
• Gorenstein properties of simple gluing algebras
• Universal Deformation Rings for Complexes over Finite-Dimensional Algebras
• On Singular Equivalences of Morita Type and Universal Deformation Rings for Gorenstein Algebras