Rank 2 arithmetically Cohen–Macaulay bundles on a nonsingular cubic surface

Rank 2 indecomposable arithmetically Cohen–Macaulay bundles E on a nonsingular cubic surface X in P3 are classified, by means of the possible forms taken by the minimal graded free resolution of E over P3. The admissible values of the Chern classes of E are listed and the vanishing locus of a general section of E is studied.Properties of E such as slope (semi)stability and simplicity are investigated; the number of relevant families is computed together with their dimension.