English

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

Complex Variables 2016-09-07 v1 Algebraic Geometry

Abstract

We construct a (non K\"ahler) compact complex 3-dimensional manifold XX having two following properties: 1) for any domain DD in C2C^2 every meromorphic map ff from this domain into XX extends to a meromorphic map from the envelope of meromorphy D^\hat D of DD into XX; 2) but there exist a meromorphic map FF from a punctured ball BB_* in C3C^3 into XX 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 XX, 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