ACM bundles on del Pezzo surfaces

ACM rank 1 bundles on del Pezzo surfaces are classified in terms of the rational normal curves that they contain. A complete list of ACM line bundles is provided. Moreover, for any del Pezzo surface $X$ of degree less or equal than six and for any $n\ge 2$ we construct a family of dimension $\ge n-1$ of non-isomorphic simple ACM bundles of rank $n$ on $X$.