On the homotopy types of compact kaehler and complex projective manifolds

Claire Voisin (1)

1 IMJ - Institut de Mathématiques de Jussieu

We show that in every dimension greater than or equal to 4, there exist compact Kaehler manifolds which do not have the homotopy type of projective complex manifolds. Thus they a fortiori are not deformation equivalent to a projective manifold, which solves negatively Kodaira's problem. We give both non simply connected (of dimension at least 4) and simply connected (of dimension at least 6) such examples.

Domaines: Géométrie algébrique [math.AG]; Géométrie symplectique [math.SG]

Claire Voisin. On the homotopy types of compact kaehler and complex projective manifolds. Inventiones Mathematicae, 2004, 157, pp.329-343. ⟨hal-00021780⟩