Equidistribution of Fekete points on complex manifolds

We prove the several variable version of the classical equidistribution theorem for Fekete points of a compact subset of the complex plane, which settles a well-known conjecture in pluri-potential theory. The result is obtained as a special case of a general equidistribution theorem for Fekete points in the setting of a given holomorphic line bundle over a compact complex manifold. The proof builds on our recent work “Capacities and weighted volumes for line bundles”.