Embedding subsets of tori Properly into ℂ 2

Erlend Fornæss Wold[1]

  • [1] University of Oslo Department of Mathematics P.O. Box 1053, Blindern 0316 Oslo (Norway)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 5, page 1537-1555
  • ISSN: 0373-0956

Abstract

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Let 𝕋 be a complex one-dimensional torus. We prove that all subsets of 𝕋 with finitely many boundary components (none of them being points) embed properly into ℂ 2 . We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.

How to cite

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Wold, Erlend Fornæss. "Embedding subsets of tori Properly into $\mathbb{C}^2$." Annales de l’institut Fourier 57.5 (2007): 1537-1555. <http://eudml.org/doc/10269>.

@article{Wold2007,
abstract = {Let $\mathbb\{T\}$ be a complex one-dimensional torus. We prove that all subsets of $\mathbb\{T\}$ with finitely many boundary components (none of them being points) embed properly into $\mathbb\{C\}^2$. We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.},
affiliation = {University of Oslo Department of Mathematics P.O. Box 1053, Blindern 0316 Oslo (Norway)},
author = {Wold, Erlend Fornæss},
journal = {Annales de l’institut Fourier},
keywords = {Holomorphic embeddings; Riemann surfaces; holomorphic embeddings},
language = {eng},
number = {5},
pages = {1537-1555},
publisher = {Association des Annales de l’institut Fourier},
title = {Embedding subsets of tori Properly into $\mathbb\{C\}^2$},
url = {http://eudml.org/doc/10269},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Wold, Erlend Fornæss
TI - Embedding subsets of tori Properly into $\mathbb{C}^2$
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 5
SP - 1537
EP - 1555
AB - Let $\mathbb{T}$ be a complex one-dimensional torus. We prove that all subsets of $\mathbb{T}$ with finitely many boundary components (none of them being points) embed properly into $\mathbb{C}^2$. We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.
LA - eng
KW - Holomorphic embeddings; Riemann surfaces; holomorphic embeddings
UR - http://eudml.org/doc/10269
ER -

References

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