# Projectivity of Kähler manifolds – Kodaira’s problem

Séminaire Bourbaki (2005-2006)

- Volume: 48, page 55-74
- ISSN: 0303-1179

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topHuybrechts, Daniel. "Projectivity of Kähler manifolds – Kodaira’s problem." Séminaire Bourbaki 48 (2005-2006): 55-74. <http://eudml.org/doc/252176>.

@article{Huybrechts2005-2006,

abstract = {Every compact Kähler surface is deformation equivalent to a projective surface. In particular, topologically Kähler surfaces and projective surfaces cannot be distinguished. Kodaira had asked whether this continues to hold in higher dimensions. We explain the construction of a series of counter-examples due to C. Voisin, which yields compact Kähler manifolds of dimension at least four whose rational homotopy type is not realized by any projective manifold.},

author = {Huybrechts, Daniel},

journal = {Séminaire Bourbaki},

keywords = {homotopie des variétés kählériennes compactes},

language = {eng},

pages = {55-74},

publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},

title = {Projectivity of Kähler manifolds – Kodaira’s problem},

url = {http://eudml.org/doc/252176},

volume = {48},

year = {2005-2006},

}

TY - JOUR

AU - Huybrechts, Daniel

TI - Projectivity of Kähler manifolds – Kodaira’s problem

JO - Séminaire Bourbaki

PY - 2005-2006

PB - Association des amis de Nicolas Bourbaki, Société mathématique de France

VL - 48

SP - 55

EP - 74

AB - Every compact Kähler surface is deformation equivalent to a projective surface. In particular, topologically Kähler surfaces and projective surfaces cannot be distinguished. Kodaira had asked whether this continues to hold in higher dimensions. We explain the construction of a series of counter-examples due to C. Voisin, which yields compact Kähler manifolds of dimension at least four whose rational homotopy type is not realized by any projective manifold.

LA - eng

KW - homotopie des variétés kählériennes compactes

UR - http://eudml.org/doc/252176

ER -

## References

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- [11] C. Voisin – “Hodge theory and the topology of compact Kähler and complex projective manifolds”, Lecture Notes for the Seattle AMS Summer Institute.
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