Abstract

Consider the blow up pi:(X) over tilde --> X of a complex surface X at a point. Let (E) over tilde be a holomorphic bundle on (X) over tilde whose restriction to the exceptional divisor is O(j) + O(-j), and define E = (pi,(E) over tilde)(VV). Friedman and Morgan gave the following bounds for the second Chern classes j less than or equal to c(2)((E) over tilde) - c(2)(E) less than or equal to j(2). We show that these bounds are sharp.