Chern Classes of Bundles over Rational Surfaces

الأصل · EN

Consider the blow up π: X → X of a rational surface X at a point. Let V be a holomorphic bundle over X whose restriction to the exceptional divisor equals O(j) ⊕ O(-j) and define V =(π*V). Friedman and Morgan gave the following bounds for the second Chern classes j ≤ c₂(V) - c₂(V) ≤ j². We show that these bounds are sharp.