On the homotopy types of Kaehler manifolds and the birational Kodaira problem

Details On the homotopy types of Kaehler manifolds and the birational Kodaira problem On the homotopy types of Kaehler manifolds and the birational Kodaira problem

2004-10-03

arxiv.org/abs/math/0410040v1

Mathematics

Algebraic Geometry

Scientific paper

We recently constructed examples of compact Kaeler manifolds which do not have the homotopy type of a projective complex manifold. They were however obtained by blowing-up certain complex tori, which are themselves deformation equivalent to complex projective manifolds. Thus it remained possible that in higher dimension, a birational version of Kodaira's theorem still holds. We construct however in this paper compact Kaehler manifolds, no birational model of which has the homotopy type of a projective manifold.

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