Exceptional modules over wild canonical algebras

We show that ‘‘almost all’’ exceptional modules over wild canonical algebra $\mathrm{\Lambda }$ can be described by matrices having coefficients ${\lambda }_i-{\lambda }_j$, where ${\lambda }_i,{\lambda }_j$ are elements from the parameter sequence. The proof is based on Schofield induction for sheaves in the associated categories of weighted projective lines and an extended version of C. M. Ringel’s proof for the ${}^{\mathrm{\prime }\mathrm{\prime }}0,1^{\mathrm{\prime }\mathrm{\prime }}$ matrix property for exceptional representations for finite acyclic quivers.