Arithmetically Cohen–Macaulay bundles and sets of points on general surfaces

The first Chern class of an initialized rank 2 bundle determines its level of stability. We determine bounds for numbers c1>0c1>0 such that, on a general   surface X⊂P3X⊂P3 of degree d≥4d≥4, there exists a rank 2 indecomposable (stable) aCM bundle E on X  , with first Chern class c1(E)=c1c1(E)=c1.