Motivated by the Kähler-Einstein problem and a conjecture of Yau relating to Bergman metrics, Tian studied the following problem. Let be a line bundle over a Kähler manifold , and fix a hermitian bundle metric whose curvature form is a Kähler form on . Suppose that for sufficiently large , an orthonormal set of holomorphic sections of the line bundle defines a projective embedding of . One can pull back the Fubini-Study metric to define a sequence of metrics on as increases. Tian showed that a certain rescaling of this sequence will necessarily converge in the topology to the original Kähler metric. The refined asymptotics of this sequence were taken up in a number of influential subsequent papers by other authors, and are particularly important in Simon Donaldson's program on extremal metrics. The approximability of a Kähler metric by Kähler metrics induced from projective embeddings is also relevant to Yau's picture of the Yau-Tian-Donaldson conjecture, as indicated above.