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Hartogs’ Theorem on Separate Holomorphicity for Projective Spaces

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier
Affiliation:
Département deMathématiques et de Statistique, Université de Montréal, Montréal, QC, H3C 3J7 e-mail: [email protected]
E. S. Zeron
Affiliation:
Depto. Matemáticas, CINVESTAV, México D.F., 07000, México e-mail: [email protected]
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Abstract

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

Type
Research Article
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), 335341.Google Scholar
[2] Dloussky, G., Analyticité séparée et prolongement analytique. Math. Ann. 286(1990), no. 1-3, 153168.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, 188.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. 4353.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, 8994.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. 191198.Google Scholar