Algebraic deformations of compact Kaehler surfaces.

In 1962 Kodaira proved that every compact Kaehler surface
is a deformation of an algebraic surface. His proof used
classification of surfaces and of elliptic surfaces. It
was long conjectured that the analogous result would hold
in higher dimensions, but in 2003 Voisin found examples of
compact Kaehler manifolds in all dimensions greater than
three which do not even have the same homotopy type as an
algebraic manifold, let alone are deformation-equivalent to
one. In this talk I will give a (relatively) short proof of
Kodaira's result.