ABSTRACT
An indecomposable module over a finite dimensional k-algebra is called generic if its k-dimension is infinite and it has finite length over its endomorphism ring. We show that the generic modules over a tubular algebra Λ (in the sense of Ringel) form an infinite family, naturally ordered by an index set having the order type of a closed interval of rational numbers.
We derive the result from a corresponding theorem on generic objects in the category of quasi-coherent sheaves on the weighted projective line associated to Λ. We further determine the generic objects in the associated derived category.
