Rank 2 vector bundles in a neighborhood of an exceptional curve of a smooth surface (Q1567138)

Let \(D\) be an exceptional divisor on a smooth surface and \(E\) a rank-2 vector bundle on the formal neighborhood of \(D\). The author associates to \(E\) a family of \(t\) rank-2 vector bundles \(E_i\) on \(U\) and a finite sequence of suitable pairs of integers, each pair giving the splitting type of \(E_{i|U}\). Conversely the author shows that every sequence of pairs respecting the properties of the sequence above gives rise to a rank-2 vector bundle \(E\). Its second Chern class is computed in terms of the sequence.