On the homotopy types of compact Kähler and complex projective manifolds
By Claire Voisin. 2003
101 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/36ef6b095e0ebd206266f6c548824c64d8fa7080
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In Geometry and Topology
- Claire Voisin
- G. Farkas
- M. Aprodu
- Stefan Schreieder
- Charles Vial
- D. Huybrechts
- Brendan Hassett
- M. Shen
In Mathematical Physics
- Claire Voisin
- G. Farkas
- Stefan Schreieder
- Brendan Hassett
- M. Aprodu
- Evgeny Shinder
- Kieran G. O’Grady
- Charles Vial
Citations in the corpus
- Chow Rings, Decomposition of the Diagonal, and the Topology of Families (2014, background): “Theorem (Beauville and Voisin 2004; see Theorem 5.3).”