ACM vector bundles on projective surfaces of nonnegative Kodaira dimension

Abstract

In this paper, we contribute to the construction of families of arithmetically Cohen–Macaulay (aCM) indecomposable vector bundles on a wide range of polarized surfaces [Formula: see text] for [Formula: see text] an ample line bundle. In many cases, we show that for every positive integer [Formula: see text] there exists a family of indecomposable aCM vector bundles of rank [Formula: see text], depending roughly on [Formula: see text] parameters, and in particular they are of wild representation type. We also introduce a general setting to study the complexity of a polarized variety [Formula: see text] with respect to its category of aCM vector bundles. In many cases we construct indecomposable vector bundles on [Formula: see text] which are aCM for all ample line bundles on [Formula: see text].