English

On the homotopy types of compact kaehler and complex projective manifolds

Algebraic Geometry 2015-08-14 v1 Symplectic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0312032,
  title  = {On the homotopy types of compact kaehler and complex projective manifolds},
  author = {Claire Voisin},
  journal= {arXiv preprint arXiv:math/0312032},
  year   = {2015}
}

Comments

To appear in Inventiones Math