Archivio Istituzionale della RicercaWe follow our study of non-Kähler complex structures on R4 that we defined in our previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their meromorphic functions. We also prove that the Picard groups of these complex surfaces are uncountable, and give an explicit description of the canonical bundle. Finally, we show that any connected non-compact oriented 4-manifold admits complex structures without Kähler metrics.
Non-Kähler complex structures on $\mathbbR^4$, II / Di Scala, Antonio J.; Kasuya, Naohiko; Zuddas, Daniele. - In: JOURNAL OF SYMPLECTIC GEOMETRY. - ISSN 1527-5256. - STAMPA. - 16:3(2018), pp. 631-644. [10.4310/JSG.2018.v16.n3.a2]
Non-Kähler complex structures on $\mathbbR^4$, II
Di Scala, Antonio J.;
2018
Abstract
We follow our study of non-Kähler complex structures on R4 that we defined in our previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their meromorphic functions. We also prove that the Picard groups of these complex surfaces are uncountable, and give an explicit description of the canonical bundle. Finally, we show that any connected non-compact oriented 4-manifold admits complex structures without Kähler metrics.
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https://hdl.handle.net/11583/2729942
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