Some generalizations of Schmidt's subspace theorem

TL;DR

This paper extends Schmidt's subspace theorem by providing a quantitative version for higher degree polynomials and generalizing it to families of closed subschemes in algebraic projective varieties.

Contribution

It introduces a quantitative form of Schmidt's theorem for higher degree polynomials and generalizes the theorem to arbitrary families of closed subschemes.

Findings

Quantitative bounds for higher degree polynomial cases

Generalization to arbitrary families of closed subschemes

Broader applicability in algebraic geometry

Abstract

The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary families of closed subschemes in algebraic projective varieties.