Parameter curves for the regular representations of tame bimodules

We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all tame bimodules where such a curve is actually commutative, or in different words, where the unique generic module has a commutative endomorphism ring. This extends results from [D. Kussin, Noncommutative curves of genus zero—Related to finite dimensional algebras, Mem. Amer. Math. Soc., in press] to arbitrary characteristic; in characteristic two additionally inseparable cases occur. Further results are concerned with autoequivalences fixing all objects but not isomorphic to the identity functor.