About the hyperbolicity of complete intersections

TL;DR

This paper surveys the relationship between Kobayashi hyperbolicity and positivity of the canonical bundle in projective algebraic varieties, highlighting recent developments and open problems in the field.

Contribution

It provides an overview of the connections between hyperbolicity and positivity properties of canonical bundles, emphasizing recent advances and open questions.

Findings

Survey of hyperbolicity and positivity relations

Highlights recent progress in the field

Identifies open problems and future directions

Abstract

This note is an extended version of a thirty minutes talk given at the "XIX Congresso dell'Unione Matematica Italiana", held in Bologna from September 12th to September 17th, 2011. This was essentially a survey talk about connections between Kobayashi hyperbolicity properties and positivity properties of the canonical bundle of projective algebraic varieties.