Hartogs’ Theorem on Separate Holomorphicity for Projective Spaces
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 84-86

Voir la notice de l'article provenant de la source Cambridge University Press

If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic.
DOI : 10.4153/CMB-2009-010-8
Mots-clés : 32A10, 32D99, 32H99, separately holomorphic, projective space
Gauthier, P. M.; Zeron, E. S. Hartogs’ Theorem on Separate Holomorphicity for Projective Spaces. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 84-86. doi: 10.4153/CMB-2009-010-8
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[1] [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] [2] Dloussky, G., Analyticité séparée et prolongement analytique. Math. Ann. 286(1990), no. 1-3, 153–168. Google Scholar

[3] [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] [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] [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] [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

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