Hyperbolicity of the complement of plane algebraic curves

TL;DR

This paper proves that the complement of certain generic plane algebraic curves, specifically three quadrics or two quadrics and a line, is hyperbolic, supporting Kobayashi's conjecture for degree five curves.

Contribution

It establishes the hyperbolicity of the complement of a generic configuration of three quadrics and two quadrics with a line, advancing the understanding of Kobayashi's conjecture.

Findings

Complement of three quadrics is hyperbolic.

Complement of two quadrics and a line is hyperbolic.

Supports conjecture that degree five curves have hyperbolic complements.

Abstract

The paper is a contribution of the conjecture of Kobayashi that the complement of a generic plain curve of degree at least five is hyperbolic. The main result is that the complement of a generic configuration of three quadrics is hyperbolic and hyperbolically embedded as well as the complement of two quadrics and a line.