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 P^3 are classified, by means of the possible forms taken by the minimal graded free resolution of E over P^3.   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 (semi) stability and simplicity are investigated; the number of relevant families is computed together with their dimension. 
Daniele Faenzi