A generalized Schmidt's subspace theorem for algebraic points of bounded degree

TL;DR

This paper extends Schmidt's subspace theorem to algebraic points of bounded degree using Seshadri constants and joint weights, providing a more general and sharp version of the theorem.

Contribution

It introduces a generalized Schmidt's theorem for algebraic points of bounded degree based on Seshadri constants and joint weights, expanding previous results.

Findings

Derived a new version of Schmidt's subspace theorem for algebraic points of bounded degree.

Utilized Seshadri constants to sharpen the theorem in the context of ample divisors.

Provided a joint weights approach to generalize the theorem.

Abstract

Schmidt's subspace theorem in terms of Seshadri constants for closed subschemes in subgeneral position has been already developed sharply. We derive our theorem for numerically equivalent ample divisors by dint of the above theory step by step, providing a joint weights version of generalized Schmidt's theorem for algebraic points of bounded degree.