An interpolation property of locally Stein sets. (English) Zbl 1422.32018

Vâjâitu, Viorel

Publ. Mat., Barc. 63, No. 2, 715-725 (2019); corrigendum ibid. 66, No. 1, 435-439 (2022).

Summary: We prove that, if \(D \) is a normal open subset of a Stein space \(X\) of pure dimension such that \(D\) is locally Stein at every point of \(\partial D \setminus X_{\mathrm{sg}}\), then, for every holomorphic vector bundle \(E\) over \(D\) and every discrete subset \(\Lambda \) of \(D \setminus X_{\mathrm{sg}}\) whose set of accumulation points lies in \(\partial D \setminus X_{\mathrm{sg}}\), there is a holomorphic section of \(E\) over \(D\) with prescribed values on \(\Lambda\). We apply this to the local Steinness problem and domains of holomorphy.

MSC:

32E10

Stein spaces

Keywords:

Stein space; domain of holomorphy; \(\overline \partial\)-problem