Claude LeBrun
Topology versus Chern numbers for complex 3-folds

We show by example that the Chern numbers c₁³ and c₁c₂ of a complex 3-fold are not determined by the topology of the underlying smooth compact 6-manifold. In fact, we observe that infinitely many different values of a Chern number can be achieved by (integrable) complex structures on a fixed 6-manifold.