Chern Classes of Bundles over Rational Surfaces

Abstract

Consider the blow up $\pi :\tilde{X}\to X$ of a rational surface $X$ at a point. Let $\tilde{V}$ be a holomorphic bundle over $\tilde{X}$ whose restriction to the exceptional divisor equals ${\cal{O}(j) \oplus {\cal O}(-j)$ and define $V=({\pi }_{\ast }\tilde{V}{)}^{\vee \vee }.$ Friedman and Morgan gave the following bounds for the second Chern classes $j\le c_2(\tilde{V})-c_2(V)\le j^2.$ We show that these bounds are sharp.

A mistake in the original was corrected