# 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.

## Key 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.