Algebraic degeneracy theorem for holomorphic mappings into smooth projective algebraic varieties

Source abstract

The famous Picard theorem states that a holomorphic mapping f : C → P 1 ( 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 P n ( 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.