An extension of the derivative of meromorphic functions to holomorphic curves
Let \(f: \mathbb{C}\to P^ n(\mathbb{C})\) be a holomorphic curve and \[ (f_ 1,f_ 2,\dots, f_{n_ 1}): \mathbb{C}\to \mathbb{C}^{n+1}\backslash \{0\} \] be a reduced representation of \(f\). The author introduces a sort of derivative to holomorphic curves as follows: Let \(W(f_ 1,f_ 2,\dots, f_{n+1})\) be the Wronskian of \(f_ 1,f_ 2,\dots, f_{n+1}\), then the derived holomorphic curve of \(f\), denoted by \(f^*\), is the mapping \[ (f^{n+1}_ 1,\dots, f^{n+1}_ n,\;W(f_ 1,\dots, f_{n+1})): \mathbb{C}\to \mathbb{C}^{n+1}. \] The author proves that \(f^*\) possesses some similar properties to the derivative of meromorphic functions.
scientific article; zbMATH DE number 701473