Proper holomorphic embeddings with small limit sets

Forstnerič, Franc (author)

Let $X$ be a Stein manifold of dimension $n\ge 1$. Given a continuous positive increasing function $h$ on ${\mathbb R}_+ = [0,\infty)$ with $\lim_{t\to\infty} h(t)=\infty$, we construct a proper holomorphic embedding $f=(z,w):X \hookrightarrow {\mathbb C}^{n+1}\times {\mathbb C}^n$ satisfying $|w(x)|<h(|z(x)|)$ for all $x\in X$. In particular, $f$ may be chosen such that its limit set at infinity is a linearly embedded copy of $\mathbb{CP}^n$ in $\mathbb{CP}^{2n}$.

• Language: English
• Keywords: Stein manifold, proper holomorphic embedding
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2024
• Year: 2024
• Number of pages: Str. 77-83
• Numbering: Vol. 11
• PID: 20.500.12556/RUL-156187
• UDC: 517.5
• ISSN on article: 2330-1511
• DOI: 10.1090/bproc/212
• COBISS.SI-ID: 195187203
• Publication date in RUL: 13.05.2024

Record is a part of a journal

• Title: Proceedings of the American Mathematical Society : Series B
• Shortened title: Proc. Am. Math. Soc., Ser. B
• Publisher: American Mathematical Society
• ISSN: 2330-1511
• COBISS.SI-ID: 520264217

Licences

• License: CC BY 3.0, Creative Commons Attribution 3.0 Unported
• Link: https://creativecommons.org/licenses/by/3.0/deed.en
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Secondary language

• Language: Slovenian
• Keywords: Steinova mnogoterost, prava holomorfna vložitev