kato surfaces
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Author(s):  
Nicolina Istrati ◽  
Alexandra Otiman ◽  
Massimiliano Pontecorvo

Abstract We revisit Brunella’s proof of the fact that Kato surfaces admit locally conformally Kähler 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 that admit no locally conformally Kähler 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 Kähler manifolds with algebraic dimension $n-2$, algebraic reduction bimeromorphic to $\mathbb{C}\mathbb{P}^{n-2}$, and admitting nontrivial holomorphic vector fields.



2019 ◽  
Vol 138 ◽  
pp. 33-43
Author(s):  
Akira Fujiki ◽  
Massimiliano Pontecorvo


2018 ◽  
Vol 12 (1-2) ◽  
pp. 239-249
Author(s):  
Massimiliano Pontecorvo


2015 ◽  
Vol 91 ◽  
pp. 117-130 ◽  
Author(s):  
Akira Fujiki ◽  
Massimiliano Pontecorvo
Keyword(s):  


2014 ◽  
Vol 58 ◽  
pp. 251-261
Author(s):  
M. Brunella
Keyword(s):  


2014 ◽  
Vol 64 (3) ◽  
pp. 1331-1361 ◽  
Author(s):  
Adolfo Guillot
Keyword(s):  


2011 ◽  
Vol 202 ◽  
pp. 77-81 ◽  
Author(s):  
Marco Brunella

AbstractWe show that every Kato surface admits a locally conformally Kähler metric.



2011 ◽  
Vol 202 ◽  
pp. 77-81 ◽  
Author(s):  
Marco Brunella

AbstractWe show that every Kato surface admits a locally conformally Kähler metric.





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