Open AccessHolomorphic curves omitting five planes in projective space
Author(s) -
Alexandre Erëmenko
Publication year - 1996
Publication title -
american journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.818
H-Index - 67
eISSN - 1080-6377
pISSN - 0002-9327
DOI - 10.1353/ajm.1996.0048
Subject(s) - mathematics , holomorphic function , conjecture , counterexample , pure mathematics , projective plane , complex projective space , projective space , mathematical analysis , projective test , combinatorics , geometry , correlation
In 1928 H. Cartan proved an extension of Montel's normality criterion to holomorphic curves in the complex projective plane P2. He also conjectured that a similar result is true for holomorphic curves in Pn for any n. Recently, the author constructed a counterexample to this conjecture for any n ≥ 3. In this paper we show how to modify Cartan's conjecture so that it becomes true, at least for n = 3.
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