1998/04/02 by Sergei Ivashkovich, Ivashkovich, Sergei
Mathematics · #14E05 #14J30 #32D15 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14E05 #msc:14J30 #msc:32D15
paper · pdf · doi:10.48550/arxiv.math/9804009
To appear in Amer. J. Math
arxiv created 1998/04/02 · arxiv updated 2016/09/07
We construct a (non Kähler) compact complex 3-dimensional manifold X having two following properties: 1) for any domain D in C2 every meromorphic map f from this domain into X extends to a meromorphic map from the envelope of meromorphy D of D into X; 2) but there exist a meromorphic map F from a punctured ball B_* in C3 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.