# A zoo of symplectic, complex and non Kähler manifolds

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Giovanni Bazzoni
(Università degli Studi dell'Insubria)

created by daniele on 28 Mar 2015

modified on 27 Apr 2015

15 may 2015
-- 16:20

Sala Conferenze, Collegio Puteano, Pisa

**Abstract.**

(Joint work with M. Fernández and V. Muñoz).

The goal of this talk is to give an overview of the existing examples of manifolds which are symplectic and complex but carry no Kähler metric.
I will also construct an example of a simply connected manifold which admits both symplectic and complex structures, but no Kähler structure. Such a manifold has dimension 6, the lowest in which such a phenomenon can occurr.

*References*

{BFM} G. Bazzoni, M. Fernández and V. Muñoz, *A 6-dimensional simply connected complex and symplectic manifold with no Kähler metric*, http://arxiv.org/abs/1410.6045, *preprint*.