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arXiv · 1511.08471

Non-Kähler complex structures on $R^4$ II

Antonio J. Di Scala·Naohiko Kasuya·Daniele Zuddas
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Abstract

We follow our study of non-Kähler complex structures on $R^4$ that we defined in a 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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Antonio J. Di Scala, Naohiko Kasuya, Daniele Zuddas. 2016-10-05. Non-Kähler complex structures on $R^4$ II. https://doi.org/10.4310/jsg.2018.v16.n3.a2

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