Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T16:54:30.327Z Has data issue: false hasContentIssue false
  • English
  • Français

Hartogs’ Theorem on Separate Holomorphicity for Projective Spaces

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier  and
E. S. Zeron
P. M. Gauthier
Affiliation:
Département deMathématiques et de Statistique, Université de Montréal, Montréal, QC, H3C 3J7 e-mail: gauthier@dms.umontreal.ca
E. S. Zeron
Affiliation:
Depto. Matemáticas, CINVESTAV, México D.F., 07000, México e-mail: eszeron@math.cinvestav.mx
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic.

Keywords

32A1032D9932H99separately holomorphicprojective space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 84 - 86
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Alexander, H., Taylor, B. A., and Ullman, J. L., Areas of projections of analytic sets. Invent. Math. 16(1972), 335–341.Google Scholar
[2] Dloussky, G., Analyticité séparée et prolongement analytique. Math. Ann. 286(1990), no. 1-3, 153–168.Google Scholar
[3] Hartogs, F., Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen, insbesondere über die Darstellung derselben durch Reihen, welche nach Potenzen einer Veränderlichen fortschreiten. Math. Ann 62(1906), no. 1, 1–88.Google Scholar
[4] Hai, Le Mau and Khue, Nguyen Van, Hartogs spaces, spaces having the Forelli property and Hartogs holomorphic extension spaces. Vietnam J. Math. 33(2005), no. 1, pp. 43–53.Google Scholar
[5] Shiffman, B., Hartogs theorems for separately holomorphic mappings into complex spaces. C. R. Acad. Sci. Paris Sér. I Math. 310(1990), no. 3, 89–94.Google Scholar
[6] Shiffman, B., Separately meromorphic functions and separately holomorphic mappings. In: Several Complex Variables and Complex Geometry. Proc. Sympos. Pure Math. 52, American Mathematical Society, Providence, RI, 1991, pp. 191–198.Google Scholar