Moduli of map germs, Thom polynomials and the Green-Griffiths conjecture

TL;DR

This survey explores the moduli of holomorphic map germs from the complex line into compact manifolds, linking global singularity theory and hyperbolic algebraic varieties, and discusses Thom polynomials and the Green-Griffiths conjecture.

Contribution

It provides a comprehensive overview of the moduli of map germs and their applications to singularity theory and hyperbolic geometry, highlighting recent developments.

Findings

Connections between map germ moduli and hyperbolic varieties

Applications of Thom polynomials in singularity classification

Insights into the Green-Griffiths conjecture

Abstract

This survey paper is based on my IMPANGA lectures given in the Banach Center, Warsaw in January 2011. We study the moduli of holomorphic map germs from the complex line into complex compact manifolds with applications in global singularity theory and the theory of hyperbolic algebraic varieties.