On a class of Kato manifolds
| Autor: | Istrati, Nicolina, Otiman, Alexandra, Pontecorvo, Massimiliano |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | We revisit Brunella's proof of the fact that Kato surfaces admit locally conformally K\" ahler metrics, and we show that it holds for a large class of higher dimensional complex manifolds containing a global spherical shell. On the other hand, we construct manifolds containing a global spherical shell which admit no locally conformally K\"ahler metric. We consider a specific class of these manifolds, which can be seen as a higher dimensional analogue of Inoue-Hirzebruch surfaces, and study several of their analytical properties. In particular, we give new examples, in any complex dimension $n \geq 3$, of compact non-exact locally conformally K\" ahler manifolds with algebraic dimension $n-2$, algebraic reduction bimeromorphic to $\mathbb{C}\mathbb{P}^{n-2}$ and admitting non-trivial holomorhic vector fields. Comment: extended version; some terminology issues are fixed; main results are improved; section added concerning the algebraic reduction; expository changes |
| Databáze: | arXiv |
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