Degeneracy of holomorphic maps via orbifolds

TL;DR

This paper employs orbifold structures to establish degeneracy results for holomorphic maps into logarithmic surfaces, improving previous smooth case results and extending them to singular pairs with applications to nodal surfaces and singular plane curve complements.

Contribution

It introduces a novel approach using orbifold structures to generalize degeneracy theorems for holomorphic maps into singular pairs and logarithmic surfaces.

Findings

Improved degeneracy results for smooth cases.

Extended degeneracy statements to singular pairs.

Applications to nodal surfaces and singular plane curves.

Abstract

We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.