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Titlebook: Several Complex Variables VII; Sheaf-Theoretical Me H. Grauert,Th. Peternell,R. Remmert Book 1994 Springer-Verlag Berlin Heidelberg 1994 Co

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978-3-642-08150-7Springer-Verlag Berlin Heidelberg 1994
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Cohomology,Cohomology (with values in a sheaf) — attaching to every sheaf ℒ of abelian groups “cohomology groups” H.(X, ℒ), q ≥ 0 — was invented in the late 1940s but implicitly it has been present since the 19th century. We want to explain this and demonstrate the necessity for a cohomology theory at the hand of several classical or “basic” problems.
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Seminormal Complex Spaces,Section 1 deals with the notion of analytically branched coverings. The main theorem states that analytically branched coverings are normal complex spaces. Its proof makes use of L.-methods as developed by Hörmander, and is sketched in § 2. In § 3 some applications are given, some of which are used in § 7.
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Differential Calculus, Holomorphic Maps and Linear Structures on Complex Spaces,he main themes are: differential calculus, structure of holomorphic maps of complex spaces, formal completions and, finally, special classes of complex spaces (Cohen-Macaulay) and dualizing sheaves. Since these subjects are quite different in nature, we describe the sections separately.
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H. Grauert,Th. Peternell,R. Remmertt zu werden verdient. Die erste Perspektive — man könnte sie die des unbefangenen Blicks nennen — erschließt die thematischen und strukturellen Gemeinsamkeiten, die das Werk beider Autoren verknüpft; die zweite — die der historischen Korrektur — vermittelt die Einsicht in die tiefgreifenden Differen
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