Hartogs' theorem on separate holomorphicity for projective spaces

2006/07/20 by P. M. Gauthier, Gauthier, P. M., E. S. Zeron +1
Mathematics · #32A10 #32D99 #32H99 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32A10 #msc:32D99 #msc:32H99

paper · pdf · doi:10.48550/arxiv.math/0607503

3 pages

arxiv created 2006/07/20 · arxiv updated 2009/12/01

Abstract

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

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• A unified approach to the theory of separately holomorphic mappings
• A geometrical proof of the Hartogs extension theorem
• Elementary approach to the Hartogs extension theorem
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• Hartogs companions and holomorphic extensions in arbitrary dimension