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arXiv · 2301.00473

Stein neighborhood bases of embedded strongly pseudoconvex domains and approximation of mappings

Tadej Starčič
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Abstract

In this paper we construct a Stein neighborhood basis for any compact subvariety $A$ with strongly pseudoconvex boundary $bA$ and Stein interior $A\backslash bA$ in a complex space $X$. This is an extension of a well known theorem of Siu. When $A$ is a complex curve, our result coincides with the result proved by Drinovec-Drnov\v{s}ek and Forstneri\v{c}. We shall adapt their proof to the higher dimensional case, using also some ideas of Demailly's proof of Siu's theorem. For embedded strongly pseudoconvex domain in a complex manifold we also find a basis of tubular Stein neighborhoods. These results are applied to the approximation problem for holomorphic mappings.

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Tadej Starčič. 2023-01-01. Stein neighborhood bases of embedded strongly pseudoconvex domains and approximation of mappings. https://arxiv.org/abs/2301.00473

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