An Extension of the Cartan-Nochka Second Main Theorem for Hypersurfaces

TL;DR

This paper extends the Cartan-Nochka Second Main Theorem to holomorphic curves in complex projective varieties intersecting hypersurfaces in subgeneral position, broadening the theorem's applicability.

Contribution

It generalizes Nochka's theorem from hyperplanes in projective space to hypersurfaces in complex projective varieties, accommodating subgeneral position.

Findings

Generalization of Nochka's theorem to complex projective varieties

Applicable to hypersurfaces in subgeneral position

Broadens understanding of defect relations in complex geometry

Abstract

In 1983, Nochka proved a conjecture of Cartan on defects of holomorphic curves in CP^n relative to a possibly degenerate set of hyperplanes. In this paper, we generalize the Nochka's theorem to the case of curves in a complex projective variety intersecting hypersurfaces in subgeneral position.