A generalization of effective schmidt's subspace theorem for projective varieties over function fields

TL;DR

This paper extends Schmidt's subspace theorem to smooth projective varieties over function fields, providing an effective version for hypersurfaces in m-subgeneral position, thereby generalizing previous results.

Contribution

It introduces an effective form of Schmidt's subspace theorem applicable to a broader class of varieties and hypersurfaces over function fields, improving upon earlier work.

Findings

Effective version of Schmidt's subspace theorem established

Generalization to hypersurfaces in m-subgeneral position

Improves upon previous results by An-Wang, Ru-Wang, and the author

Abstract

We establish an effective version of Schmidt's subspace theorem on a smooth projective variety $\mathcal{X}$ over function fields of characteristic zero for hypersurfaces located in m-subgeneral position with respect to $\mathcal{X}$. Our result generalizes and improves the results of An-Wang, Ru-Wang and the author.