ACM bundles on del Pezzo surfaces

TL;DR

This paper classifies ACM rank 1 bundles on del Pezzo surfaces using rational normal curves and constructs large families of higher-rank ACM bundles on certain del Pezzo surfaces, advancing the understanding of their bundle structures.

Contribution

It provides a complete classification of ACM line bundles on del Pezzo surfaces and constructs large families of non-isomorphic simple ACM bundles of higher rank.

Findings

Complete list of ACM line bundles on del Pezzo surfaces.

Construction of large families of higher-rank ACM bundles.

Classification in terms of rational normal curves.

Abstract

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 $n\geq 2$ we construct a family of dimension $\geq n-1$ of non-isomorphic simple ACM bundles of rank $n$ on $X$.