Abstract

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence {E-i}(1less than or equal toiless than or equal tot) of rank 2 vector bundles canonically associated to E. We calculate numerical invariants of E in terms of the splitting types of E-i, 1less than or equal toiless than or equal tot. If S is a compact complex smooth surface and E is a rank two bundle on the blow-up of S at a point, we show that all values of c(2)(E) - c(2)(pi,(E)**) that'are numerically possible are actually attained.