On Maximal Green Sequence for Quivers Arising from Weighted Projective Lines

We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let Q be Gabriel quiver endomorphism algebra a basic cluster-tilting object in cluster category \(\mathcal {C}_{\mathbb {X}}\) line \(\mathbb {X}\). It is proved that there exists \(Q^{\prime }\) mutation equivalence class Mut(Q) such admits sequence. Furthermore, which does not admit sequence if only {X}\) wild type.