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Zbl 0845.14007
Ran, Ziv
Hodge theory and deformations of maps. (English)
[J] Compos. Math. 97, No.3, 309-328 (1995). ISSN 0010-437X; ISSN 1570-5846/e

The paper under review is an abstraction of previous results of the authors into the most general (non)-sensical context. The general idea, formulated in vague terms, is that the image of a Hodge-type group under a functorial homomorphism into an infinitesimal deformation group lands in the unobstructed deformations. Dually given a functorial homomorphism from an obstruction group into a Hodge type group, the effective obstructions lie in the kernel.\par As applications the author considers deformations of maps, especially immersions (generalizing a result by C. Voisin to general $q$-symplectic complex manifolds, to the effect that the deformation spaces of Lagrangian immersions are smooth) and fiber spaces. The author concludes by considering conditions for curves to move, getting results for symplectic $n$-folds, and considering the structure of Kähler manifolds, whose bundles of holomorphic two-forms are spanned outside a finite set of points.
[U.Persson (Göteborg)]

MSC 2000:: *14C30 Transcendental methods

Keywords: base change; formal schemes; Hodge-type group; unobstructed deformations

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