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In his 1928 thesis H. Cartan proved a theorem which can be considered as an extension of Montel’s normality criterion to holomorphic curves in complex projective plane      P 2 \mathbf {P}^2      . He also conjectured that a similar result is true for holomorphic curves in      P n \mathbf {P}^n       for any      n n      . A counterexample to this conjecture is constructed for any      n ≥  3 n\geq 3      .

A counterexample to Cartan’s conjecture on holomorphic curves omitting hyperplanes