Holomorphic mappings between spaces of different dimensions. II
In this part II of the paper [part I: the author, ibid. 214, No. 4, 567- 577 (1993; see the paper above)], the author proves the following result: Let \(f: \mathbb{C} \to N\) be a holomorphic mapping into a pseudo canonical complex projective variety \(N\). Then either \(f\) is algebraically degenerate or the image of \(f\) is autoparallel with respect to a meromorphic connection on \(N\). By using the result, we can prove a classical conjecture as follows: Let \(f: \mathbb{C} \to W\subset \mathbb{P}^ n\) be a holomorphic map to a hypersurface of degree at least \(n+2\). Then \(f\) is algebraically degenerate.
scientific article; zbMATH DE number 567396
scientific article