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 OeM, and ωxo the sheaf of (1,O)-forms over Xo. The family π defines an element ζπ∈(Ext1 (ΩXo, ℋo))x for every point xeX. 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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