On the homotopy types of compact Kahler and complex projective manifolds

摘要

The celebrated Kodaira Theorem [6] says that a compact complex manifold is projective if and only if it admits a Koler form whose cohomology class is integral. This suggests that Koler geometry is an extension of projective geometry, obtained by relaxing the integrality condition on a Koler class. This point of view, together with the many restrictive conditions on the topology of Koler manifolds provided by Hodge theory (the strongest one being the formality theorem [4]), would indicate that compact Koler manifolds and complex projective ones cannot be distinguished by topological invariants.