Weak normality of families of meromorphic mappings and bubbling in higher dimensions

Details Weak normality of families of meromorphic mappings and bubbling in higher dimensions Weak normality of families of meromorphic mappings and bubbling in higher dimensions

2011-04-20

arxiv.org/abs/1104.3973v1

Mathematics

Complex Variables

25 pages

Scientific paper

We recall several natural notions of convergence of meromorphic mappings between general complex manifolds and give a precise analytic description of them in the case when the target manifold is projective. We also prove the Bloch-Montel type normality criterion for the so called weak convergence. Furthermore we determine the structure of the exceptional components of the limit of a weakly converging sequence - they turn out to be rationally connected. An application to the Fatou sets of meromorphic self-maps of compact complex surfaces is given.

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