Proper holomorphic embeddings with small limit sets
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917823610093568 |
|---|---|
| author | Forstneric, Franc |
| author_facet | Forstneric, Franc |
| contents | 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 $\mathbb{CP}^{2n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Proper holomorphic embeddings with small limit sets Forstneric, Franc Complex Variables Primary 32H02, Secondary 32E10, 32Q56 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 $\mathbb{CP}^{2n}$. |
| title | Proper holomorphic embeddings with small limit sets |
| topic | Complex Variables Primary 32H02, Secondary 32E10, 32Q56 |
| url | https://arxiv.org/abs/2310.19396 |