A generalized subspace theorem for closed subschemes in subgeneral position

TL;DR

This paper extends a recent theorem in Diophantine approximation and Nevanlinna theory to include closed subschemes in subgeneral position, broadening the scope of existing theorems using a new technique.

Contribution

It introduces a generalized subspace theorem for closed subschemes in subgeneral position, expanding previous results with a novel approach based on generic linear combinations.

Findings

Extended the subspace theorem to subgeneral position cases

Unified approach for Diophantine and Nevanlinna theory results

Broadened applicability of the theorem to more complex geometric configurations

Abstract

In this paper, we extend the recent theorem of G. Heier and A. Levin [arXiv:1712.02456] on the generalization of Schmidt's subspace theorem and Cartan's Second Main Theorem in Nevanlinna theory to closed subschemes located in $l$-subgeneral position, using the generic linear combination technique due to Quang.