On base point free theorem for log canonical threefolds over the algebraic closure of a finite field

TL;DR

This paper proves a key algebraic geometry theorem for three-dimensional log canonical pairs over algebraically closed finite fields, extending the understanding of line bundles and their base point freeness.

Contribution

It establishes the base point free theorem for big line bundles on log canonical threefolds over algebraic closures of finite fields, a case previously unresolved.

Findings

Proved the base point free theorem in this setting.

Extended the theorem to three-dimensional log canonical pairs.

Enhanced understanding of line bundles over finite fields.

Abstract

We prove the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field.