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Algebraic degeneracy theorem for holomorphic mappings into smooth projective algebraic varieties

Published online by Cambridge University Press:  22 January 2016

Yoshihiro Aihara  and
Seiki Mori
Yoshihiro Aihara
Affiliation:
Mathematical Institute, Tôhoku University, Sendai, 980, Japan
Seiki Mori
Affiliation:
Mathematical Institute, Tôhoku University, Sendai, 980, Japan
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The famous Picard theorem states that a holomorphic mapping f: C → P1(C) omitting distinct three points must be constant. Borel [1] showed that a non-degenerate holomorphic curve can miss at most n + 1 hyperplanes in Pn(C) in general position, thus extending Picard’s theorem (n = 1). Recently, Fujimoto [3], Green [4] and [5] obtained many Picard type theorems using Borel’s methods for holomorphic mappings.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 84 , December 1981 , pp. 209 - 218
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[ 1 ] Borel, E., Sur les zéros des fonctions entières, Acta Math., 20 (1896), 357–396.Google Scholar
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