A truncated second main theorem for algebraic tori with moving targets and applications

TL;DR

This paper proves a second main theorem for algebraic tori with moving targets of slow growth, leading to applications in the Green-Griffith-Lang conjecture and exponential polynomial integrability.

Contribution

It introduces a new second main theorem for algebraic tori with moving targets and applies it to key problems in complex geometry and exponential functions.

Findings

Proved the Green-Griffith-Lang conjecture for projective spaces with moving targets.

Established a second main theorem with truncation at level 1 for algebraic tori.

Discussed the integrability of exponential polynomials in entire functions.

Abstract

We establish a second main theorem for algebraic tori with slow growth moving targets with truncation to level 1. As the first application of this result, we prove the Green-Griffith-Lang conjecture for projective spaces with $n+1$ components in the context of moving targets of slow growth. Then we discuss the integrability of the ring of exponential polynomials in the ring of entire functions as another application.