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Réduction d’Albanèse d’un morphisme propre et faiblement Kählerian. I, II: Groupes d’automorphismes relatifs. (French) Zbl 0609.32008
A relative torus is a morphism \(T\to S\) of reduced analytic spaces which is, generically on S, a submersion whose fibers are affine complex tori. The Albanese reduction of a proper surjective morphism \(X\to S\) is a relative torus \(A\to S\) such that each morphism of (X,S) in a relative torus factorizes uniquely through (A,S).
In the first paper, the author establishes the existence of the Albanese reduction for a proper surjective, weakly Kählerian morphism. In the second paper, he introduces the notion of relative automorphism group of a proper surjective morphism and establishes the existence of decomposition into linear and toroidal parts for the relative automorphism group of a weakly Kählerian morphism. He studies also the obstruction to algebraicity for morphisms with algebraic fibers.
Reviewer: G.Roos

MSC:
32C15 Complex spaces
32M99 Complex spaces with a group of automorphisms
32J99 Compact analytic spaces
14E99 Birational geometry
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