%0 Journal Article %T Surfaces of minimal degree of tame and wild representation type %A Daniele Faenzi %A Francesco Malaspina %J Mathematics %D 2014 %I arXiv %X We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands. %U http://arxiv.org/abs/1409.4892v3