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January 2006 On the homotopy types of Käahler manifolds and the birational Kodaira problem
Claire Voisin
J. Differential Geom. 72(1): 43-71 (January 2006). DOI: 10.4310/jdg/1143593125

Abstract

Previously, we constructed examples of compact Kähler 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, saying that a compact Kähler surface deforms to a projective surface, still holds. We construct in this paper compact Kähler manifolds, no smooth birational model of which, however, has the homotopy type of a projective manifold. Thus the possibility mentioned above is excluded, even at the topological level.

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Claire Voisin. "On the homotopy types of Käahler manifolds and the birational Kodaira problem." J. Differential Geom. 72 (1) 43 - 71, January 2006. https://doi.org/10.4310/jdg/1143593125

Information

Published: January 2006
First available in Project Euclid: 28 March 2006

zbMATH: 1102.32008
MathSciNet: MR2215455
Digital Object Identifier: 10.4310/jdg/1143593125

Rights: Copyright © 2006 Lehigh University

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Vol.72 • No. 1 • January 2006
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