Chern Classes of Bundles over Rational Surfaces

Details Chern Classes of Bundles over Rational Surfaces Chern Classes of Bundles over Rational Surfaces

1997-11-15

arxiv.org/abs/alg-geom/9711018v2

Mathematics

Algebraic Geometry

A mistake in the original was corrected

Scientific paper

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

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