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Familien komplexer räume zu gegebenen infinitesimalen deformationen

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Abstract

Let M be a domain in the complex plane, π:X→M a flat family of reduced complex spaces, (Xo, ℋo) the fibre over a point OεM, and ωxo the sheaf of (1,O)-forms over Xo. The family π defines an element ζπ∈(Ext1 (ΩXo, ℋo))x for every point xεX. We prove: If (Xo, ℋo) is a normal complex space, x a point in Xo such that (Ext2 (ΩXo, ℋo))x=O, then for each infinitesimal deformation ζ∈(Ext1 (ΩXo, ℋo))x there exists a flat reduced family π with ζπ=ζ. This statement is analogous to a result of KODAIRA-NIRENBERG-SPENCER in the theory of deformations of compact complex manifolds.

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  1. Mathematisches Institut der Universität, Schellingstraße 2-8, 8000, München 13

    Hans Kerner

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  1. Hans Kerner
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Kerner, H. Familien komplexer räume zu gegebenen infinitesimalen deformationen. Manuscripta Math 1, 317–337 (1969). https://doi.org/10.1007/BF01172140

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