On the homotopy types of compact kaehler and complex projective manifolds
Voisin, Claire
HAL, hal-00021780 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],  [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] 
@article{hal-00021780,
     author = {Voisin, Claire},
     title = {On the homotopy types of compact kaehler and complex projective manifolds},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00021780}
}

Voisin, Claire. On the homotopy types of compact kaehler and complex projective manifolds. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00021780/