Simply connected Voisin manifolds of dimension four

Linsheng Wang

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3699-3710

Abstract: Voisin constructed a series of examples of simply connected compact Kähler manifolds of even dimension, 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 do not have the rational homotopy type of a complex projective manifold. Oguiso constructed simply connected compact Kähler manifolds starting from dimension four, which cannot 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.

Date: 2023
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https://doi.org/10.1002/mana.202200066

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