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arXiv · 2108.07957

Dimension four simply connected Voisin manifolds

Linsheng Wang
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Abstract

Voisin constructed a series of examples concerning simply connected compact K\"ahler manifolds of even dimensions, which do not have the rational homotopy type of a complex projective manifold starting from dimension six. In this note, we prove that Voisin's examples of dimension four also does not have the rational homotopy type of a complex projective manifold. Oguiso constructed simply connected compact K\"ahler manifolds starting from dimension four, which can not deform to a complex projective manifold under a small deformation. We also prove that Oguiso's examples do not have the rational homotopy type of a complex projective manifold.

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Linsheng Wang. 2021-08-18. Dimension four simply connected Voisin manifolds. https://arxiv.org/abs/2108.07957

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