One example in concern with extension and separate analyticity properties of meromorphic mappings
Abstract
We construct a (non K\"ahler) compact complex 3-dimensional manifold having two following properties: 1) for any domain in every meromorphic map from this domain into extends to a meromorphic map from the envelope of meromorphy of into ; 2) but there exist a meromorphic map from a punctured ball in into which doens't extend meromorphically to the origin. In other words, one can allways remove the singularities of complex codimesion two for the meromorphic maps into this , but only up to some subset of complex codimension three. A description of the appearing obstructions in the terms of Lelong numbers is given. Further some applications of the techniques, developped in this paper, to the questions of separate analyticity are also described.
Keywords
Cite
@article{arxiv.math/9804009,
title = {One example in concern with extension and separate analyticity properties of meromorphic mappings},
author = {Sergei Ivashkovich},
journal= {arXiv preprint arXiv:math/9804009},
year = {2016}
}
Comments
To appear in Amer. J. Math