A geometric second main theorem

TL;DR

This paper establishes a new version of the second main theorem in complex geometry, specifically for entire curves in the projective plane that tend to cluster on algebraic curves, advancing the understanding of value distribution.

Contribution

It introduces a truncated second main theorem tailored for entire curves in the projective plane that cluster on algebraic curves, providing new insights into their value distribution properties.

Findings

Proves a truncated second main theorem for entire curves in the projective plane.

Shows clustering behavior of entire curves on algebraic curves.

Advances the theoretical framework of value distribution in complex geometry.

Abstract

We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.