Exceptional sequences for canonical algebras (Q1805514)

Let \(\Lambda\) be a canonical algebra with \(n\) simple modules and \({\mathcal D}^ b(\text{mod}(\Lambda))\) the derived category of right \(\Lambda\)- modules. We show that the semidirect product of \(\mathbb{Z}^ n\) and the braid group on \(n\) strings acts transitively on the set of exceptional sequences in \({\mathcal D}^ b(\text{mod}(\Lambda))\). Similar results are proved for coherent sheaves on weighted projective lines.