A $6$-dimensional simply connected complex and symplectic manifold with no K\"ahler metric
Symplectic Geometry
2014-11-17 v2 Algebraic Geometry
Differential Geometry
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.
Keywords
Cite
@article{arxiv.1410.6045,
title = {A $6$-dimensional simply connected complex and symplectic manifold with no K\"ahler metric},
author = {Giovanni Bazzoni and Marisa Fernández and Vicente Muñoz},
journal= {arXiv preprint arXiv:1410.6045},
year = {2014}
}
Comments
14 pages, no figures. Second version: minor changes in the introduction, exposition clarified and new references added. Comments are welcome!