The methods of the theory of functions of several complex variables.

*(English)*Zbl 0737.32001
Miscellanea mathematica, Festschr. H. Götze, 129-143 (1991).

[For the entire collection see Zbl 0723.00017.]

The author describes the development of complex analysis from the beginning of the century to the present time. He begins with the Hartogs figure and then he discusses pseudo-convex domains, the Weierstrass preparation theorem, Cousin problems, coherent sheaves, nonreduced complex spaces, isolated singularities, Moishezon spaces, connections with algebraic geometry, Hodge theory, negative line bundles and many other problems. The article is written with mastership, very clearly, with sketches of some proofs or with indications of the methods used, it is described how problems and notions lead naturally to other ones, for what purpose some methods were introduced. This gives a good idea of complex analysis in general for a non-specialist and every person interested in the subject should read this article!

The author describes the development of complex analysis from the beginning of the century to the present time. He begins with the Hartogs figure and then he discusses pseudo-convex domains, the Weierstrass preparation theorem, Cousin problems, coherent sheaves, nonreduced complex spaces, isolated singularities, Moishezon spaces, connections with algebraic geometry, Hodge theory, negative line bundles and many other problems. The article is written with mastership, very clearly, with sketches of some proofs or with indications of the methods used, it is described how problems and notions lead naturally to other ones, for what purpose some methods were introduced. This gives a good idea of complex analysis in general for a non-specialist and every person interested in the subject should read this article!

Reviewer: K.Dabrowski (Piastow)

##### MSC:

32-02 | Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces |

32Dxx | Analytic continuation |

32Fxx | Geometric convexity in several complex variables |

32Hxx | Holomorphic mappings and correspondences |

32Jxx | Compact analytic spaces |

32Lxx | Holomorphic fiber spaces |

01A60 | History of mathematics in the 20th century |

32Axx | Holomorphic functions of several complex variables |

32Bxx | Local analytic geometry |

32Cxx | Analytic spaces |