We construct a simply connected compact manifold which has complex and symplectic structures but does not admit K"ahler metrics, in the lowest possible dimension where this can happen, that is, dimension 6. Such a manifold is automatically formal and has even odd-degree Betti numbers but it does not satisfy the Lefschetz property for any symplectic form.

A 6-dimensional simply connected complex and symplectic manifold with no Kähler metric

Bazzoni G;
2018-01-01

Abstract

We construct a simply connected compact manifold which has complex and symplectic structures but does not admit K"ahler metrics, in the lowest possible dimension where this can happen, that is, dimension 6. Such a manifold is automatically formal and has even odd-degree Betti numbers but it does not satisfy the Lefschetz property for any symplectic form.
2018
https://www.intlpress.com/site/pub/pages/journals/items/jsg/content/vols/0016/0004/a004/index.html
symplectic non Kahler manifold; symplectic resolution
Bazzoni, G; Fernández, M; Muñoz, V
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2086825
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