An effective uniform Artin-Rees lemma

TL;DR

This paper establishes a global uniform Artin-Rees lemma for sections of ample line bundles on smooth projective varieties, and applies it to polynomial rings with uniform degree bounds using multidimensional residue calculus.

Contribution

It introduces a new global uniform Artin-Rees lemma and extends it to polynomial rings with uniform degree bounds, utilizing multidimensional residue calculus.

Findings

Proved a global uniform Artin-Rees lemma for ample line bundle sections.

Extended the lemma to polynomial rings with uniform degree bounds.

Used multidimensional residue calculus in the proof.

Abstract

We prove a global uniform Artin-Rees lemma type theorem for sections of ample line bundles over smooth projective varieties. This result is used to prove an Artin-Rees lemma for the polynomial ring with uniform degree bounds. The proof is based on multidimensional residue calculus.