Volume 106, Issue 4 p. 3670-3686
RESEARCH ARTICLE

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

Ji Guo

Corresponding Author

Ji Guo

School of Mathematics and Statistics, Central South University, Changsha, China

Correspondence

Ji Guo, School of Mathematics and Statistics, Central South University, Changsha 410075, China.

Email: [email protected]

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Chia-Liang Sun

Chia-Liang Sun

Institute of Information Science, Academia Sinica, Nankang, Taipei, Taiwan

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Julie Tzu-Yueh Wang

Julie Tzu-Yueh Wang

Institute of Mathematics, Academia Sinica, Taipei, Taiwan

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First published: 22 August 2022

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 $n+1$ 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.