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