# Entire Curves in Algebraic Varieties

• Junjiro Noguchi
• Jörg Winkelmann
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 350)

## Abstract

In Chap.  the Second Main Theorem for differentiably non-degenerate meromorphic mappings f:C m V into a projective algebraic manifold V of dimVm was established in a satisfactory form. It is the next problem to deal with the case of m<dimV. In this case the freeness of the images inside V is very large, and causes the difficulties. It is still an open problem to establish the general Second Main Theorem in the case of m<dimV. We take the typical case of m=1 in this chapter. In the first half we will show the Cartan–Nochka Second Main Theorem for V=P n (C). The readers who first learn the theory of holomorphic curves in P n (C) should skip Sect. 4.1 and are recommended to read Sect. 4.2, assuming that holomorphic curves are linearly non-degenerate and the given hyperplanes are in general position; in this case, N=n, ω(j)=1, and $$\tilde{\omega}=1$$.

## Keywords

Meromorphic Function Complex Manifold Holomorphic Curve Weighted Degree Entire Curve
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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