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

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-Griffiths-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.