Séminaires : Séminaire d'Algèbre

This is a report on joint work with D. Labardini-Fragoso and J. Schröer. We show that for most marked surfaces with non-empty boundary, possibly with punctures, the generic Caldero-Chapoton functions form a basis of the corresponding cluster algebras for any choice of geometric coefficients. For surfaces without punctures the $\tau$-reduced components of the corresponding gentle Jacobian algebra are naturally parametrized by X-laminations of the surface, and it is easy to see that for principal coefficients, the generic basis coincides with the bangle basis introduced by Musiker-Schiffler-Williams.