Representation type of rational ACM surfaces X ⊆ P4

The goal of this work is to determine the representation type of any smooth rational ACM surface in 4 by constructing large families of simple Ulrich bundles of arbitrary rank. It turns out that, excluding the cubic scroll, all of them are of wild representation type. In addition, we show that a general linear standard determinantal variety of codimension one or two supports indecomposable Ulrich sheaves of rank 1 and 2. © 2012 Springer Science+Business Media B.V