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

Abstract:

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 $\mathbf {P}^2$. He also conjectured that a similar result is true for holomorphic curves in $\mathbf {P}^n$ for any $n$. A counterexample to this conjecture is constructed for any $n\geq 3$.