One example in concern with extension and separate analyticity properties of meromorphic mappings

Details One example in concern with extension and separate analyticity properties of meromorphic mappings One example in concern with extension and separate analyticity properties of meromorphic mappings

1998-04-02

arxiv.org/abs/math/9804009v1

Mathematics

Complex Variables

To appear in Amer. J. Math

Scientific paper

We construct a (non K\"ahler) compact complex 3-dimensional manifold $X$ having two following properties: 1) for any domain $D$ in $C^2$ every meromorphic map $f$ from this domain into $X$ extends to a meromorphic map from the envelope of meromorphy $\hat D$ of $D$ into $X$; 2) but there exist a meromorphic map $F$ from a punctured ball $B_*$ in $C^3$ into $X$ 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 $X$, 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.

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